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# M17-37

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Math Expert
Joined: 02 Sep 2009
Posts: 56303

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16 Sep 2014, 01:02
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Difficulty:

15% (low)

Question Stats:

78% (01:38) correct 22% (01:55) wrong based on 232 sessions

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Andrew and Stephen drive on the highway in the same direction at respective rates of 72 and 80 kmh. If Stephen is 4 km behind Andrew, by how much does he have to increase his speed to catch up with Andrew in 20 minutes?

A. 1 kmh
B. 2 kmh
C. 3 kmh
D. 4 kmh
E. 5 kmh

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16 Sep 2014, 01:02
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Official Solution:

Andrew and Stephen drive on the highway in the same direction at respective rates of 72 and 80 kmh. If Stephen is 4 km behind Andrew, by how much does he have to increase his speed to catch up with Andrew in 20 minutes?

A. 1 kmh
B. 2 kmh
C. 3 kmh
D. 4 kmh
E. 5 kmh

Denote the required acceleration as $$x$$. The distance between Andrew and Stephen will be decreasing at $$(80 + x - 72)$$ kmh. We can compose the equation $$\frac{4}{80 + x - 72} = \frac{20}{60}$$ from which $$x = 4$$.

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29 Jan 2017, 19:24
hi Bunuel

Thnx
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Joined: 02 Sep 2009
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30 Jan 2017, 00:32
gupta87 wrote:
hi Bunuel

Thnx

Check other solutions here: https://gmatclub.com/forum/andrew-and-s ... 77984.html

Hope it helps.
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GMAT 1: 740 Q49 V42
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31 May 2017, 06:32
20x=4

x=1/5

x/60 = 1/5

x=12

12-8 = 4

D

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Joined: 08 Jun 2015
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31 May 2017, 06:45
The answer has to be option D.

The distance between Andrew and Stephen is 4 Km. We need to find the quantum by which Stephen needs to increase his speed to catch up with Andrew.

4/(x-72)=1/3. Solving for x , we get 84. Andrew needs to increase his speed by 4kmph.
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31 May 2017, 09:55
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In 20 minutes Andrew would cover 72*20/60=24 which means Stephen has to cover 28 km in 20 mins
let the increased speed be x
(80+x)*20/60=28
=>x=4
hence D
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31 May 2017, 11:10
1
If Stephen has to take a lead of 4 km in 20 minutes, it means he has to take a lead of 12 km in 60 minutes (or 1 hour)
(Just multiplied both with 3, to calculate in km/h)

So their relative speed needs to be 12 km/h. Stephen is right now at 80 km/h and Andrew at 72 km/h. Their relative speed as of now is (80-72) = 8 km/h. So Stephen needs to further increase his speed by (12-8) = 4 km/h

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23 Aug 2018, 20:08
Andrew and Stephen drive on the highway in the same direction at respective rates of 72 and 80 kmh. If Stephen is 4 km behind Andrew, by how much does he have to increase his speed to catch up with Andrew in 20 minutes?

In 20 minutes Andrew can cover (72/3) = 24km. But since he is ahead by 4 km, total distance covered = 24 + 4 = 28km.
In 20 minutes, if Stephen needs to cover 28km, his speed must be 28*3 = 84km/hr. Therefore, he must increase by 4km/hr.
Re: M17-37   [#permalink] 23 Aug 2018, 20:08
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# M17-37

Moderators: chetan2u, Bunuel