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Andrew and Stephen are driving on a highway in the same direction at

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bigfernhead
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Andrew and Stephen are driving on a highway in the same direction at [#permalink] New post   22 Apr 2009, 17:49
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Andrew and Stephen are driving on a highway in the same direction at speeds of 72 km/h and 80 km/h, respectively. If Stephen is 4 km behind Andrew, by how much must he increase his speed to catch up with Andrew in 20 minutes?

A. 1 km/h
B. 2 km/h
C. 3 km/h
D. 4 km/h
E. 5 km/h

M17-37

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D
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benpack03
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Re: Andrew and Stephen are driving on a highway in the same direction at [#permalink] New post   25 Jul 2009, 13:42
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I think its much easier to first assume that they are going the same speed. So he has to catch up 4 meters in 1/3 hour. r= d/t = 4/(1/3) = 12 km/hr faster he has to go. He is already going 8km/h faster, so 12 - 8 = 4 km/hr
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Andrew and Stephen are driving on a highway in the same direction at [#permalink] New post   19 Oct 2014, 02:58
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Andrew and Stephen are driving on a highway in the same direction at speeds of 72 km/h and 80 km/h, respectively. If Stephen is 4 km behind Andrew, by how much must he increase his speed to catch up with Andrew in 20 minutes?

A. 1 km/h
B. 2 km/h
C. 3 km/h
D. 4 km/h
E. 5 km/h


Let's assume Stephen needs to increase his speed by \(x\) km/h, which means he would drive at \(80 + x\) km/h. The relative speed between Stephen and Andrew would then be \(80 + x - 72\) km/h. To close the 4 km gap, the time required would be \(\frac{distance}{speed} = \frac{4}{80 + x - 72}\) hours. Since this time should be 1/3 of an hour (or 20 minutes), we have the equation \(\frac{4}{80 + x - 72} = \frac{1}{3}\). Solving for \(x\), we find \(x = 4\).

Answer: D.
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Re: Andrew and Stephen are driving on a highway in the same direction at [#permalink] New post   22 Apr 2009, 18:44
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A -- 72 Kmh
B -- 80 Kmh

Relative speed = 8 kmh

distance b/w them = 4 Km

4 /( 80 +x - 72) = 20/60

solve for x = 4 .....

Ans . D
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Re: Andrew and Stephen are driving on a highway in the same direction at [#permalink] New post   02 May 2009, 07:36
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If x is the distance travelled by Andrew in 20 minutes = 72*20/60 = 24km

Stephen's speed would to travel (24+4)km = 28*60/20 = 84 km/h

So, answer is D - 4km/h
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Re: Andrew and Stephen are driving on a highway in the same direction at [#permalink] New post   02 May 2009, 15:25
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relative speed=80-72=8
need to catch up 4km

currently Stephen is catching up at a speed of 4km/30mins, or 2km/15mins
he needs to increase the speed, so that he can make 4km in 20 mins instead, or 1km/5mins

x - the relative speed increase we seek
2/15+x=1/5
x=1/15

So, he needs to increase relative speed by 1km per 15mins, or 4km/h
Therefore, the answer is D.
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Re: Andrew and Stephen are driving on a highway in the same direction at [#permalink] New post   03 Feb 2017, 12:47
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bigfernhead wrote:
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



We can classify this problem as a “catch-up” rate problem, for which we use the formula:

distance of Andrew + 4 = distance of Stephen

We are given that Andrew is driving at a rate of 72 kmh and that Stephen is driving at a rate of 80 kmh. We need to determine how much faster Stephen needs to drive to catch up to Andrew in 20 minutes or 20/60 = 1/3 hour.

If we let r = Stephen’s speed increase, we can say the following:

distance of Stephen = (r + 80)(1/3) = (r + 80)/3

distance of Andrew + 4 = 72 x 1/3 + 4 = 28

We can equate the two distances and determine r.

(r + 80)/3 = 28

r + 80 = 84

r = 4

Answer: D
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Andrew and Stephen are driving on a highway in the same direction at [#permalink] New post   23 Dec 2023, 02:45
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bigfernhead wrote:
Andrew and Stephen are driving on a highway in the same direction at speeds of 72 km/h and 80 km/h, respectively. If Stephen is 4 km behind Andrew, by how much must he increase his speed to catch up with Andrew in 20 minutes?

A. 1 km/h
B. 2 km/h
C. 3 km/h
D. 4 km/h
E. 5 km/h

M17-37

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This is simply a relative speed problem. 4 km needs to be covered within 20 mins i.e. 1/3rd of an hour.

So relative speed required \(= \frac{4}{1/3} = 12 km/hr\)

Andrew's speed is 72 km/hr so Stephen speed should be 12 km/hr more than this i.e. Stephen's speed should be 84 km/hr. Stephen's current speed is 80 km/hr so he should increase his speed by 4 km/hr

Answer (D)

Check these videos for relative speed:
https://youtu.be/EDsHa_CULmg
https://youtu.be/wrYxeZ2WsEM
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Andrew and Stephen are driving on a highway in the same direction at [#permalink]
23 Dec 2023, 02:45
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