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Two runners’ race times sum to 170 seconds and one of the ra

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Two runners’ race times sum to 170 seconds and one of the ra [#permalink] New post 14 Jun 2018, 14:13
Expert's post
00:00

Question Stats:

88% (01:19) correct 11% (01:33) wrong based on 9 sessions
Two runners’ race times sum to 170 seconds and one of the race times is 10 seconds less than twice the other. What is the faster race time, in seconds?

(A) 40
(B) 50
(C) 60
(D) 70
(E) 110
[Reveal] Spoiler: OA

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Intern
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Joined: 02 May 2018
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Re: Two runners’ race times sum to 170 seconds and one of the ra [#permalink] New post 16 Jun 2018, 13:37
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Runner 1 = X
Runner 2 = Y

Two runners’ race times sum to 170 seconds translates to
\(x+y=170\)

one of the race times is 10 seconds less than twice the other translates to
\(y=2x-10\)

Here we have a system of equations, and you can substitute y in the original equation.

\(x+2x-10=170\)
\(3x=180\)
\(x=60\)

The answer is C.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1664 [0], given: 396

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Re: Two runners’ race times sum to 170 seconds and one of the ra [#permalink] New post 05 Jul 2018, 01:48
Expert's post
Explanation

Call the race times x and y. The question provides a sum: x + y = 170.

One of the race times is 10 seconds less than twice the other: x = 2y – 10.

Since the second equation is already solved for x, plug (2y – 10) in for x in the first equation:

\(2y - 10 + y = 170\)

\(3y - 10 = 170\)

\(3y = 180\)

\(y = 60\)

If y = 60 and the times sum to 170, then x = 110.

Note that the question asks for the faster race time—that means the smaller number! The answer is 60.

Hence option C is correct!
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Re: Two runners’ race times sum to 170 seconds and one of the ra   [#permalink] 05 Jul 2018, 01:48
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Two runners’ race times sum to 170 seconds and one of the ra

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