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Shannon and Maxine work in the same building and leave work 15 May 2012, 10:39
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D
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Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46
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D
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Shannon and Maxine work in the same building and leave work 16 May 2012, 09:49
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alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46
Show more

Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.
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Shannon and Maxine work in the same building and leave work 16 May 2012, 03:03
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alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46
Show more

Say Maxine lives \(d\) miles from office, then Shannon lives \(60-d\) miles from office.

If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon --> \(\frac{d}{2r}=\frac{60-d}{2r}+\frac{2}{3}\) --> \(3d=90+2r\);

If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine --> \(\frac{d}{r}=\frac{60-d}{2r}+2\) --> \(3d=60+4r\);

Solve \(3d=90+2r\) and \(3d=60+4r\) for \(d\) --> \(d=40\).

Answer: D.
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Shannon and Maxine work in the same building and leave work Updated on: 09 Apr 2014, 08:53
Originally posted by jlgdr on 31 Dec 2013, 10:24.
Last edited by jlgdr on 09 Apr 2014, 08:53, edited 1 time in total.
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Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46
Show more

Nice question +1

We have that X/24 - (60-X)/2R = 40

Also X/R - (60-X)/2R = 120

So we get that 2x - 60 = 80R
3x - 60 = 240R

Get rid of R

120 = 3x
x = 40

Hence answer is D

Hope it helps
Cheers!
J :)

Y'all also, one can do the following

(X/2R)-(60-X/2R) = 2/3

(X/R)-(60-X/2R)=2

Therefore we have the following pair of equations:

6x-180=4r (1)
3x-60=4r (2)

Therefore we can equate both and obtain x=40.

Hence D

Hope it helps
Cheers
J :)
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Shannon and Maxine work in the same building and leave work 15 Feb 2014, 00:00
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VeritasPrepKarishma
alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.
Show more


Hi Karishma,

You mentioned time difference between time1 and time 2 is 80 mins... How dod you take the value for time1 as 80 mins?
Please explain the basis.

ThNks
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Shannon and Maxine work in the same building and leave work 28 Jan 2015, 10:20
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VeritasPrepKarishma
alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.

Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.
Show more



Hi Karisma,

You have an interesting approach. However, I am not sure if I understand you well here. Maxine reaches 2 hrs after Shanon. So Maxine should take 120 min more and not 1 hr 20 min (=80 min). Am I correct? If yes, how will your proposed solution change? Can you please explain?

TO
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Shannon and Maxine work in the same building and leave work 28 Jan 2015, 10:25
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jlgdr
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Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Nice question +1

We have that X/24 - (60-X)/2R = 40

Also X/R - (60-X)/2R = 120

So we get that 2x - 60 = 80R
3x - 60 = 240R

Get rid of R

120 = 3x
x = 40

Hence answer is D

Hope it helps
Cheers!
J :)

Y'all also, one can do the following

(X/2R)-(60-X/2R) = 2/3

(X/R)-(60-X/2R)=2

Therefore we have the following pair of equations:

6x-180=4r (1)
3x-60=4r (2)

Therefore we can equate both and obtain x=40.

Hence D

Hope it helps
Cheers
J :)
Show more


Hi,

In the line "We have that X/24 - (60-X)/2R = 40" of your solution, can you please clarify from where did you get 24 in the denominator?

TO
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Shannon and Maxine work in the same building and leave work 28 Jan 2015, 12:52
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thorinoakenshield
jlgdr
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Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Nice question +1

We have that X/24 - (60-X)/2R = 40

Also X/R - (60-X)/2R = 120

So we get that 2x - 60 = 80R
3x - 60 = 240R

Get rid of R

120 = 3x
x = 40

Hence answer is D

Hope it helps
Cheers!
J :)

Y'all also, one can do the following

(X/2R)-(60-X/2R) = 2/3

(X/R)-(60-X/2R)=2

Therefore we have the following pair of equations:

6x-180=4r (1)
3x-60=4r (2)

Therefore we can equate both and obtain x=40.

Hence D

Hope it helps
Cheers
J :)


Hi,

In the line "We have that X/24 - (60-X)/2R = 40" of your solution, can you please clarify from where did you get 24 in the denominator?

TO
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Should be 2R. (4 on key-koard is too close to R = typo)
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Shannon and Maxine work in the same building and leave work Updated on: 17 Oct 2022, 01:26
Originally posted by KarishmaB on 29 Jan 2015, 00:31.
Last edited by KarishmaB on 17 Oct 2022, 01:26, edited 1 time in total.
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thorinoakenshield


Hi Karisma,

You have an interesting approach. However, I am not sure if I understand you well here. Maxine reaches 2 hrs after Shanon. So Maxine should take 120 min more and not 1 hr 20 min (=80 min). Am I correct? If yes, how will your proposed solution change? Can you please explain?

TO
Show more

The solution I have given above is correct.

There are two cases: One in which both drive home - here Maxine reaches 40 mins after Shannon
In the other case, Maxine bikes and Shannon drives - here Maxine reaches 120 mins after Shannon

So difference in time taken by Maxine in the two cases is 120 mins - 40 mins = 80 mins
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Shannon and Maxine work in the same building and leave work 17 Dec 2022, 22:34
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alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Say Maxine lives \(d\) miles from office, then Shannon lives \(60-d\) miles from office.

If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon --> \(\frac{d}{2r}=\frac{60-d}{2r}+\frac{2}{3}\) --> \(3d=90+2r\);

If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine --> \(\frac{d}{r}=\frac{60-d}{2r}+2\) --> \(3d=60+4r\);

Solve \(3d=90+2r\) and \(3d=60+4r\) for \(d\) --> \(d=40\).

Answer: D.
Show more

Shouldn’t the speed of max should be 2R, in second eqn too,
But u kept it R??? When maxine cycles from 2R speed,she reaches 45 min earlier and when she cycles from R speed, she reaches 2 hours earlier???how

Shouldn’t in second equation Shannon should be R and Maxine be 2R
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Shannon and Maxine work in the same building and leave work 17 Dec 2022, 22:35
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Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Nice question +1

We have that X/24 - (60-X)/2R = 40

Also X/R - (60-X)/2R = 120

So we get that 2x - 60 = 80R
3x - 60 = 240R

Get rid of R

120 = 3x
x = 40

Hence answer is D

Hope it helps
Cheers!
J :)

Y'all also, one can do the following

(X/2R)-(60-X/2R) = 2/3

(X/R)-(60-X/2R)=2

Therefore we have the following pair of equations:

6x-180=4r (1)
3x-60=4r (2)

Therefore we can equate both and obtain x=40.

Hence D

Hope it helps
Cheers
J :)
Show more

Shouldn’t the speed of max should be 2R, in second eqn too,
But u kept it R??? When maxine cycles from 2R speed,she reaches 45 min earlier and when she cycles from R speed, she reaches 2 hours earlier???how

Shouldn’t in second equation Shannon should be R and Maxine be 2R
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Shannon and Maxine work in the same building and leave work 08 Aug 2023, 14:59
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KarishmaB
alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.
Show more


I solved this question as following:

Maxine traveled the distance from her work to her house "DM" twice, once by car at a rate 2R mph and the second time by bike at a rate R mph. Since the distance is the same, time and rate will vary inversely:
(t+2/3)/t+2 = R/2R = 1/2 (t is the time Shannon is taking to drive to her house and 2/3 hours=40 min)
From the above, we can solve for t, hence t=2/3 hours

At first, both Shannon and Maxine drove by car to their houses at the rate 2Rmph. Since the rate in this case is the same, time and distance will vary directly:
t/(t+2/3) = DS/DM (DS and DM are Shonnon and Maxine respective distances to their houses from work).
Replacing t by 2/3, we get DS/DM=1/2
Therefore,
DS:DM:TOT
1:2:3
(knowing that the actual total distance is 60, the unkown multiplier would hence be 20)
DS:DM:TOT
20:40:60

So DM= 40 and correct answer is D

Dear KarishmaB
I figured that this question can be solved algebraically as well as suggested by Bunuel above but I have been unsuccessful trying to solve this question using relative speed. Can this question be solved using relative speed to start with? If not can you please explain why?
Thank you so much!
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Shannon and Maxine work in the same building and leave work 08 Aug 2023, 23:33
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KarishmaB
alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.


I solved this question as following:

Maxine traveled the distance from her work to her house "DM" twice, once by car at a rate 2R mph and the second time by bike at a rate R mph. Since the distance is the same, time and rate will vary inversely:
(t+2/3)/t+2 = R/2R = 1/2 (t is the time Shannon is taking to drive to her house and 2/3 hours=40 min)
From the above, we can solve for t, hence t=2/3 hours

At first, both Shannon and Maxine drove by car to their houses at the rate 2Rmph. Since the rate in this case is the same, time and distance will vary directly:
t/(t+2/3) = DS/DM (DS and DM are Shonnon and Maxine respective distances to their houses from work).
Replacing t by 2/3, we get DS/DM=1/2
Therefore,
DS:DM:TOT
1:2:3
(knowing that the actual total distance is 60, the unkown multiplier would hence be 20)
DS:DM:TOT
20:40:60

So DM= 40 and correct answer is D

Dear KarishmaB
I figured that this question can be solved algebraically as well as suggested by Bunuel above but I have been unsuccessful trying to solve this question using relative speed. Can this question be solved using relative speed to start with? If not can you please explain why?
Thank you so much!
Show more

This is not a relative speed question because they are not covering the 60 miles "together."
They are each covering their own distance in their own time. Shannon arrived early and stopped while Maxine kept going.
Had they covered a certain distance together in the same time, relative speed would have come into play.
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Shannon and Maxine work in the same building and leave work 11 Aug 2023, 09:01
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was able to solve it algebraically but took 6mins ! :(
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KarishmaB
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Shannon and Maxine work in the same building and leave work 13 Aug 2023, 23:35
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GianKR
KarishmaB
alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.


I solved this question as following:

Maxine traveled the distance from her work to her house "DM" twice, once by car at a rate 2R mph and the second time by bike at a rate R mph. Since the distance is the same, time and rate will vary inversely:
(t+2/3)/t+2 = R/2R = 1/2 (t is the time Shannon is taking to drive to her house and 2/3 hours=40 min)
From the above, we can solve for t, hence t=2/3 hours

At first, both Shannon and Maxine drove by car to their houses at the rate 2Rmph. Since the rate in this case is the same, time and distance will vary directly:
t/(t+2/3) = DS/DM (DS and DM are Shonnon and Maxine respective distances to their houses from work).
Replacing t by 2/3, we get DS/DM=1/2
Therefore,
DS:DM:TOT
1:2:3
(knowing that the actual total distance is 60, the unkown multiplier would hence be 20)
DS:DM:TOT
20:40:60

So DM= 40 and correct answer is D

Dear KarishmaB
I figured that this question can be solved algebraically as well as suggested by Bunuel above but I have been unsuccessful trying to solve this question using relative speed. Can this question be solved using relative speed to start with? If not can you please explain why?
Thank you so much!
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Check this video for when to use relative speed: https://youtu.be/wrYxeZ2WsEM
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Malar95
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Shannon and Maxine work in the same building and leave work 28 Dec 2023, 23:44
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Not sure how much of my working makes sense but given that I struggle with Algebra (mental blocks), I just played around with the figures based on my understanding of the concept.
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aronbhati
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Shannon and Maxine work in the same building and leave work 01 Mar 2025, 07:23
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HI Mam,

Can you explain me after that difference between Time 1 & Time 2 is 80 minutes. How Time 1 ( Maxine ) is 80 minutes

but as per Ratio equation S1: S2>>>> 2:1 and Time 1: time 2>>>>>1:2 means time 1 is of Shannon then how Time 1 is of Maxine in your answer
KarishmaB
alexpavlos
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

A. 20
B. 34
C. 38
D. 40
E. 46

Here is the ratios approach to the problem:

Shannon drives at the speed of 2R in both the cases so she takes the same time. In the first case Maxine reaches home 40 mins after Shannon. In the second case, Maxine reaches 2 hrs after Shannon. Why did Maxine take 1 hr 20 mins extra in the second case? Because she drove at half the speed.
Speed1: Speed 2 = 2:1
Time 1: Time 2 = 1:2 ( since distance stays the same)
The difference between Time1 and Time 2 is 1 hr 20 mins = 80 mins. So Time 1 must be 1hr 20 mins i.e. time taken by Maxine when she drives at speed 2R. Time taken by Shannon must be 1 hr 20 mins - 40 mins = 40 mins (because she reaches 40 mins early)

When their speeds were same in the first case,
Time taken by Maxine : Time taken by Shannon = 80 mins :40 mins = 2:1
Distance traveled by Maxine : Distance traveled by Shannon = 2:1

Total distance is 60 miles so Maxine lives 40 miles away and Shannon lives 20 miles away from office.
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shubhim20
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Shannon and Maxine work in the same building and leave work 25 Mar 2025, 02:46
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chances of such questions coming in gmat focus
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Rickooreoisb
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Shannon and Maxine work in the same building and leave work 19 Jan 2026, 22:43
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Equation 1 is T2 - T1 = 40 mins
Equation 2 since the speed is half for M, time will be twice so 2T2 - T1 = 40
Solve to get T2 = 80 and T1 = 40
Thus ratio of distance is D2 : D1 = 2:1 and split 60 to get M distance as 40
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