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Tom drives from town A to town B, driving at a constant spee

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by BTGmoderatorDC » Sun Dec 09, 2018 9:32 pm
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Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?

A. 12
B. 20
C. 24
D. 30
E. 36

OA B

Source: Economist GMAT
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by Jay@ManhattanReview » Mon Dec 10, 2018 12:47 am
BTGmoderatorDC wrote:Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?

A. 12
B. 20
C. 24
D. 30
E. 36

OA B

Source: Economist GMAT
A -------------(60 mph)----------2d miles ------------B-----(x mph)-----d miles ------C

Given the average speed from A to C = 36, we have

Time take to cover the distance from A to C = (2d + d)/36 = d/12 hours
Time take to cover the distance from A to B = (2d)/60 = d/30 hours
Time take to cover the distance from B to C = d/x hours

Thus, d/30 + d/x = d/12

1/30 + 1/x = 1/12

1/x = 1/12 – 1/30 = (5 – 2)/60 = 3/60 = 1/20

=> x = 20 mph.

The correct answer: B

Hope this helps!

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by GMATGuruNY » Mon Dec 10, 2018 3:09 am
BTGmoderatorDC wrote:Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?

A. 12
B. 20
C. 24
D. 30
E. 36
Let the distance between A and B = 120 miles.
Since the 120-mile distance between A and B is twice the distance between B and C, the distance between B and C = 60 miles, implying that the total distance = 120+60 = 180 miles.

Since the average speed for the 120-mile leg between A and B = 60 mph, the time to travel from A to B = d/r = 120/60 = 2 hours.
Since the average speed for the entire 180-mile trip = 36 mph, the time to travel the entire trip = d/r = 180/36 = 5 hours.

Time to travel from B to C = (time for the entire trip) - (time to travel from A to B) = 5-2 = 3 hours.
Since it takes 3 hours to travel the 60-mile leg between B and C, the driving speed from B to C = d/t = 60/3 = 20 mph.

The correct answer is B.
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by fskilnik@GMATH » Mon Dec 10, 2018 4:06 am
BTGmoderatorDC wrote:Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?

A. 12
B. 20
C. 24
D. 30
E. 36
Source: Economist GMAT
Perfect opportunity for UNITS CONTROL, one of the most powerful tools of our method!
$$LCM\left( {36,60} \right) = 180\,\,\,\,\left\{ \matrix{
\,A \to C\,\,\,:\,\,\,180\,\,{\rm{miles}}\,\,\,\left( {{{1\,\,{\rm{hour}}} \over {36\,\,{\rm{miles}}}}} \right)\,\,\,\,\, = \,\,\,5\,\,{\rm{hours}}\, \hfill \cr
\,A \to B\,\,\,:\,\,\,{2 \over 3}\left( {180\,\,{\rm{miles}}} \right)\left( {{{1\,\,{\rm{hour}}} \over {60\,\,{\rm{miles}}}}} \right)\,\,\, = \,\,2\,\,{\rm{hours}}\,\,\, \hfill \cr
B \to C\,\,\,:\,\,\,\,\,\,\,\,?\,\, = \,\,{{{1 \over 3}\left( {180\,\,{\rm{miles}}} \right)} \over {5 - 2\,\,{\rm{hours}}}}\,\,\, = \,\,\,\,20\,\,{\rm{mph}} \hfill \cr} \right.\,\,\,$$

This solution follows the notations and rationale taught in the GMATH course.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Scott@TargetTestPrep » Fri Mar 15, 2019 5:38 pm
BTGmoderatorDC wrote:Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?

A. 12
B. 20
C. 24
D. 30
E. 36

OA B

Source: Economist GMAT
We can let the distance between B and C = d, and thus the distance between A and B = 2d. We can let r = Tom's speed driving from B to C, in miles per hour, and create the equation:

(2d + d)/(2d/60 + d/r) = 36

3d/(d/30 + d/r) = 36

3d = 36d/30 + 36d/r

3 = 6/5 + 36/r

Multiplying both sides of the equation by 5r, we have:

15r = 6r + 180

9r = 180

r = 20

Answer: B

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