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# Andrew and Stephen drive on the highway in the same direction at respe

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Retired Moderator
Joined: 18 Jul 2008
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Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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22 Apr 2009, 16:49
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Difficulty:

25% (medium)

Question Stats:

79% (01:32) correct 21% (01:51) wrong based on 487 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

M17-37
[Reveal] Spoiler: OA

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Senior Manager
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Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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22 Apr 2009, 17:44
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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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Intern
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Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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02 May 2009, 06:36
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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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Manager
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Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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02 May 2009, 14:25
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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

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Manager
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Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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25 Jul 2009, 12:42
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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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Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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19 Oct 2014, 01:58
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Expert's post
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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

M17-37

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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Director
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Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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12 Nov 2015, 19:04
4k/8kph=1/2h
4k/(8+x)kph=1/3h
x=4kph faster

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Target Test Prep Representative
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Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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03 Feb 2017, 11:47
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Expert's post
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This post was
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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

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

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Manager
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Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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03 Nov 2017, 10:17
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

M17-37

given
4/8 = 1/2

to make it 1/3, we need to change 8 to 12
so the difference is 4

thanks

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Manager
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Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
Re: Andrew and Stephen drive on the highway in the same direction at respe [#permalink]

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04 Nov 2017, 20:35
Relative speed = 8 kmh

distance b/w them = 4 Km

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

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Naveen
email: nkmungila@gmail.com
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Re: Andrew and Stephen drive on the highway in the same direction at respe   [#permalink] 04 Nov 2017, 20:35
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