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M17-37

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M17-37  [#permalink]

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New post 16 Sep 2014, 00:02
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:37) correct 22% (01:50) wrong based on 199 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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Re M17-37  [#permalink]

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New post 16 Sep 2014, 00:02
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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 \(x = 4\).

Answer: D
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Re: M17-37  [#permalink]

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New post 29 Jan 2017, 18:24
hi Bunuel
please elaborate the same problem

Thnx
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Re: M17-37  [#permalink]

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New post 29 Jan 2017, 23:32
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Re: M17-37  [#permalink]

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New post 31 May 2017, 05:32
20x=4

x=1/5

x/60 = 1/5

x=12

12-8 = 4

D

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Re: M17-37  [#permalink]

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New post 31 May 2017, 05:45
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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Re: M17-37  [#permalink]

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New post 31 May 2017, 08:55
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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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Re: M17-37  [#permalink]

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New post 31 May 2017, 10:10
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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

Hence option D answer
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Re: M17-37  [#permalink]

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New post 23 Aug 2018, 19:08
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.
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Re: M17-37 &nbs [#permalink] 23 Aug 2018, 19:08
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