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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
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Joined: 06 Feb 2016
Posts: 7
Location: United Arab Emirates
Concentration: General Management, Leadership
GMAT 1: 690 Q49 V35
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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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New post 01 Jul 2016, 14:36
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%
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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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New post 26 May 2017, 12:39
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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New post 29 Jul 2019, 23:59
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Re: A's speed is 20/13 times that of B. If A and B run a race   [#permalink] 29 Jul 2019, 23:59

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