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# Jeff drove to work from this home, averaging 40 miles per ho

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Director
Joined: 29 Nov 2012
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Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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04 Sep 2013, 23:16
3
3
00:00

Difficulty:

55% (hard)

Question Stats:

72% (02:28) correct 28% (02:43) wrong based on 298 sessions

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Jeff drove to work from this home, averaging 40 miles per hour and was 12 minutes late. The next day he left home for work at the same time, took the same route, averaging 48 miles per hour, and was 7 minutes late. How far in miles is it from Jeff's home to his work?

A. 20.0
B. 24.5
C. 30.0
D. 37.5
E. 40.0
Director
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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04 Sep 2013, 23:22
3
1
fozzzy wrote:
Jeff drove to work from this home, averaging 40 miles per hour and was 12 minutes late. The next day he left home for work at the same time, took the same route, averaging 48 miles per hour, and was 7 minutes late. How far in miles is it from Jeff's home to his work?

a) 20.0
b) 24.5
c) 30.0
d) 37.5
e) 40.0

LET DISTANCE = D

if T IS REQUIRED TIME TO REACH .

T = $$\frac{D}{40} - \frac{12}{60} = \frac{D}{48} - \frac{7}{60}$$
SOLVING D = 20

hence A
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Director
Joined: 29 Nov 2012
Posts: 759
Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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04 Sep 2013, 23:41
I didn't understand the equations but great method! Please elaborate..

$$\frac{12}{60}$$ the reason you are subtracting is because its $$\frac{12 minutes}{60 minutes}$$ late?
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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04 Sep 2013, 23:48
3
fozzzy wrote:
I didn't understand the equations but great method! Please elaborate..

$$\frac{12}{60}$$ the reason you are subtracting is because its $$\frac{12 minutes}{60 minutes}$$ late?

Let say
jeff need to reach in time T.
LET distance to office = d
now first day time taken by jeff = distance/speed = d/40
this time is 12 minutes more than T
therefore T = d/40 -12/60

SIMILARLY second day time taken by jeff = d/48
This is 7 minute more than T
Therefore T = d/40-7/60

NOW EQUATING both equation of T.
$$\frac{d}{40} -\frac{12}{60} = \frac{d}{40}-\frac{7}{60}$$

solving D = 20

hope it helps
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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04 Sep 2013, 23:55
1
fozzzy wrote:
Jeff drove to work from this home, averaging 40 miles per hour and was 12 minutes late. The next day he left home for work at the same time, took the same route, averaging 48 miles per hour, and was 7 minutes late. How far in miles is it from Jeff's home to his work?

a) 20.0
b) 24.5
c) 30.0
d) 37.5
e) 40.0

You may equate distance also

i.e., 40*(t+12/60) = 48* (t+7/60)

You get t=18/60

d= 40*(18/60+12/60) = 20 miles
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Joined: 20 Dec 2012
Posts: 4
Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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05 Sep 2013, 07:30
still i didn't understood why 12/60 and 7/60.....no where they've mentioned 60min right...
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Joined: 02 Sep 2009
Posts: 51258
Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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05 Sep 2013, 07:36
1
praneeth4u wrote:
Jeff drove to work from this home, averaging 40 miles per hour and was 12 minutes late. The next day he left home for work at the same time, took the same route, averaging 48 miles per hour, and was 7 minutes late. How far in miles is it from Jeff's home to his work?

a) 20.0
b) 24.5
c) 30.0
d) 37.5
e) 40.0

still i didn't understood why 12/60 and 7/60.....no where they've mentioned 60min right...

The point is that the rates are given in miles per hour. So, we are converting 12 and 7 minutes into hours:

12 minutes = 12/60 hours.
7 minutes = 7/60 hours.

Does this make any sense?
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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06 Sep 2013, 07:27
Thank you Bunuel.... concept is clear
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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09 Sep 2013, 05:46
I tried a different method here:
I used the following thought process...if the two day trips differed in time by 5 min (12 min late vs. 7 min late), then we can set up the two time equations and set them equal to 5 min or 1/12 hrs.

d/40 - d/48 = 1/12 (5 min); common denominator is 240, so we have (6d-5d) / 240 = 1/12 hr.

if we solve for d, we get: d / 240 = 1/12; 12d = 240 therefore, d = 20 miles.

Choose A.
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Joined: 13 May 2013
Posts: 425
Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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09 Sep 2013, 08:05
1
blueseas wrote:
fozzzy wrote:
I didn't understand the equations but great method! Please elaborate..

$$\frac{12}{60}$$ the reason you are subtracting is because its $$\frac{12 minutes}{60 minutes}$$ late?

Let say
jeff need to reach in time T.
LET distance to office = d
now first day time taken by jeff = distance/speed = d/40
this time is 12 minutes more than T
therefore T = d/40 -12/60

SIMILARLY second day time taken by jeff = d/48
This is 7 minute more than T
Therefore T = d/40-7/60

NOW EQUATING both equation of T.
$$\frac{d}{40} -\frac{12}{60} = \frac{d}{40}-\frac{7}{60}$$

solving D = 20

hope it helps

I have a quick question.

For T = d/40 -12/60, why wouldn't we add 12/60 (i.e. 12 minutes) to the d/40? After all, doesn't his time increase with his slower speed of d/40?

Thanks!

Edit: I think I got it!

Let's pretend he needs to get home in 60 minutes. The time he takes on the first day works out to be 72 minutes. From this we subtract 12 minutes to even out the equation. "T" represents his time if he is on time. d/40 represents his time on the day in question (which will be greater than his regular time) and 12/60 or 7/60 represents the extra time he took, if subtracted from his slower time would represent his normal time.

Does that make sense?

First day: t = d/40 - 12/60
Second day: t = d/48 - 7/60

d/40 - 12/60 = d/48 - 7/60
d/40 = d/48 + 5/60

(LCM of 40 and 48 is 240)

d = 40*(d/48) + 40*(5/60)
d = 40d/48 + 200/60
d = 200d/240 + 800/240
d = (200d+800)/240
240d = 200d+800
40d = 800
d = 20

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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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12 Oct 2013, 06:53
d = (t + 12/60)*40
d = (t + 7/60)*48

However, I don't understand why the t's have to be same. Can someone explain?
Math Expert
Joined: 02 Sep 2009
Posts: 51258
Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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12 Oct 2013, 07:56
1
TooLong150 wrote:
d = (t + 12/60)*40
d = (t + 7/60)*48

However, I don't understand why the t's have to be same. Can someone explain?

Because t is the usual time, for which Jeff is on time at work.
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Joined: 15 Aug 2013
Posts: 54
Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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12 Oct 2013, 21:19
1
Let 't' is the usual time taken(without getting late)... Since the ration of speed in both case is 40:48 ie 5:6 , the ratio of time taken will be reverse ie 6/5. SO t+12 / t+ 7 = 6/5 giving t = 18 mins. substitute in any - D= 40*(18+12)/60 = 20 miles
divide by 60 to change into hour...
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Joined: 13 Aug 2012
Posts: 95
Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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14 Oct 2013, 21:54
Let T be the time when Jeff is not late for work

When Jeff is 12 minutes or $$\frac{1}{5} hours$$ late, $$Time= T+\frac{1}{5}$$
$$Distance= 40(T+\frac{1}{5})$$-------------------------------------------------------------------------------------(1)

When jeff is 7 minutes or $$\frac{7}{60} hours$$ late, $$Time= T+\frac{7}{60}$$
$$Distance= 48(T+\frac{7}{60})$$------------------------------------------------------------------------------------(2)

Equating (1) & (2)

$$40(T+\frac{1}{5})=48(T+\frac{7}{60})$$
$$5T+1=6T+\frac{7}{10}$$
$$T=\frac{3}{10}$$--------------------------------------------------------------------------------------------------------(3)

Putting (3) in (1)
$$Distance= 40(\frac{3}{10}+\frac{1}{5})= 20miles$$

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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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21 Apr 2014, 00:05
Since avg. speed is given in hour ; let t be be original time when Jeff covered the distance.

as we know speed=distance/time; 40(t+12/60)=x and from second 48(t+7/60)=x

equation 1 and 2 40(t+12/60)=48(t+7/60) will give t=.3

to know distance covered put t=.3 in 1st equation 40(.3+.2)=20 So (A)
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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21 Apr 2014, 02:29
Distance = Speed x Time

Equation (1)

$$d = 40 (t + \frac{12}{60})$$

Equation (2)

$$d = 48 (t+\frac{7}{60})$$

Equating (1) & (2)

$$40 (t + \frac{12}{60}) = 48 (t+\frac{7}{60})$$

$$t = \frac{18}{60}$$

Placing value of t in Equation (1)

$$d = 40 (\frac{18}{60} + \frac{12}{60})$$

$$= 40 * \frac{30}{60}$$

= 20

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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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24 Apr 2014, 03:24
40(t+12/60) = 48(t+7/60)

solve for t,
=> t = 18/60 or 3/10

now distance = speed*time
i.e. d = 40(3/10 + 1/5) = 20.
Hence, A.
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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06 Aug 2015, 05:51
Bunuel wrote:
praneeth4u wrote:
Jeff drove to work from this home, averaging 40 miles per hour and was 12 minutes late. The next day he left home for work at the same time, took the same route, averaging 48 miles per hour, and was 7 minutes late. How far in miles is it from Jeff's home to his work?

a) 20.0
b) 24.5
c) 30.0
d) 37.5
e) 40.0

still i didn't understood why 12/60 and 7/60.....no where they've mentioned 60min right...

The point is that the rates are given in miles per hour. So, we are converting 12 and 7 minutes into hours:

12 minutes = 12/60 hours.
7 minutes = 7/60 hours.

Does this make any sense?

Bunuel pls what if "The next day he left home for work at 10 min late than yesterday"
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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06 Aug 2015, 06:22
jimwild wrote:
Bunuel wrote:
praneeth4u wrote:
Jeff drove to work from this home, averaging 40 miles per hour and was 12 minutes late. The next day he left home for work at the same time, took the same route, averaging 48 miles per hour, and was 7 minutes late. How far in miles is it from Jeff's home to his work?

a) 20.0
b) 24.5
c) 30.0
d) 37.5
e) 40.0

still i didn't understood why 12/60 and 7/60.....no where they've mentioned 60min right...

The point is that the rates are given in miles per hour. So, we are converting 12 and 7 minutes into hours:

12 minutes = 12/60 hours.
7 minutes = 7/60 hours.

Does this make any sense?

Bunuel pls what if "The next day he left home for work at 10 min late than yesterday"

For the original question, let v and t be the speed and time to reach the office without any delays.

Thus distance = vt

Case 1, 12 minutes late:

vt = 40(t+12/60) ...(1)

Case 2, 7 minutes late:

vt = 48(t+7/60) ...(2)

Thus 40(t+12/60) = 48(t+7/60) ---> t = 0.3 hour. Thus the distance = 40 (0.3+12/60) = 20 miles. A is the correct answer.

Now, coming back to your question, if the question said "The next day he left home for work at 10 min late than yesterday" ---> the time that Jim would be late will now be 10+7 = 17 minutes late (as he would be 7 minutes late when he left at the same time , so he would be 17 minutes late if left his home 10 minutes later that yesterday!) and the equations will become :

40(t+12/60) = 48(t+17/60) .
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Re: Jeff drove to work from this home, averaging 40 miles per ho  [#permalink]

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09 Jan 2017, 13:44
Two equations can be created from the prompt using the D = RT equation:

(1) D = (40mi/hr)(t+ 1/5)
(2) D = (48mi/hr)(t+ 7/60)

Plug (1) into (2) --> 40t+8 = D --> 40t+8 = 48t+(28/5)

Simplify --> (40-28)/5 = 8t --> 12/5 = 8t --> 3/10 = t

Plug this back into either of the original equations (i.e. (1) or (2)) and you'll find distance to be 20 mi.

A.
Re: Jeff drove to work from this home, averaging 40 miles per ho &nbs [#permalink] 09 Jan 2017, 13:44

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