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Difficulty:
65%
(hard)
Question Stats:
72% (03:39) correct
28%
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wrong
based on 582
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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
A. 20
B. 34
C. 38
D. 40
E. 46
alexpavlos
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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alexpavlos
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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General Discussion
jlgdr
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
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Concentration: Finance
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alex1233
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
VeritasPrepKarishma
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
thorinoakenshield
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Last visit: 28 Mar 2015
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VeritasPrepKarishma
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
thorinoakenshield
Joined: 03 Jan 2015
Last visit: 28 Mar 2015
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jlgdr
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
thorinoakenshield
Should be 2R. (4 on key-koard is too close to R = typo)
thorinoakenshield
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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Bunuel
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
jlgdr
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
KarishmaB
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!
GianKR
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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Posts: 9
was able to solve it algebraically but took 6mins ! 
GianKR
Check this video for when to use relative speed: https://youtu.be/wrYxeZ2WsEM
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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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Image 4 for Q explanation.jpg [ 52.72 KiB | Viewed 7009 times ]
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
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
chances of such questions coming in gmat focus
Rickooreoisb
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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
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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