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# A's speed is 20/13 times that of B. If A and B run a race

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Intern
Joined: 06 Feb 2016
Posts: 7
Location: United Arab Emirates
GMAT 1: 690 Q49 V35
GPA: 3.2
Re: A's speed is 20/13 times that of B. If A and B run a race  [#permalink]

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01 Jul 2016, 13:36
Common Sense approach (60 secs)
A's speed -> 20/13 of B --> A's distance -> 20/13 of B (time is constant).

A runs 20 units of distance in the same time as B runs 13.
B needs to beat A by 20%, thus, we can assume race distance to be 25 units .

--->A has to run only 20 and B has to run 25.
---> In the time A runs 20, B runs only 13
----> thus, B should be given a head start of 12 (25-13)
----> 12/25 is 48%
Senior Manager
Joined: 03 Apr 2013
Posts: 275
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: A's speed is 20/13 times that of B. If A and B run a race  [#permalink]

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26 May 2017, 11:39
anarchist112 wrote:
A's speed is 20/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 20% of the length of the race?

A. 44%
B. 48%
C. 52%
D. 42%
E. 46%

Another way to visualize this..
It is given to us that
$$\frac{A_{speed}}{B_{speed}} = \frac{20}{13}$$

let the race be of 20 units.

Now..when A completes 80% of the distance of the race..B will complete 80% of his distance according to the ratio..
$$0.8*13 = 10.4$$

But what we want..is that when A completes 80% of the race..B should complete the entire race..

So the head start will be
$$20 - 10.4 = 9.6 units$$

In terms of percentage of 20 units..it is

48%(B)
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Re: A's speed is 20/13 times that of B. If A and B run a race  [#permalink]

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01 Jul 2018, 21:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A's speed is 20/13 times that of B. If A and B run a race &nbs [#permalink] 01 Jul 2018, 21:21

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