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Two runners’ race times sum to 170 seconds and one of the ra
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14 Jun 2018, 14:13
14 Jun 2018, 14:13
Expert Reply
00:00
Question Stats:
67% (01:18) correct
32% (01:39) wrong based on 52 sessions
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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
(A) 40
(B) 50
(C) 60
(D) 70
(E) 110
Re: Two runners’ race times sum to 170 seconds and one of the ra
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16 Jun 2018, 13:37
16 Jun 2018, 13:37
1
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.
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.
Re: Two runners’ race times sum to 170 seconds and one of the ra
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05 Jul 2018, 01:48
05 Jul 2018, 01:48
Expert Reply
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!
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!
