sana.noor wrote:Hayden began walking from F to G, a distance of 40 miles, at the same time Ava began walking from G to F on the same road. If Hayden’s walking speed was x miles per hour and Ava’s was y miles per hour, how many miles away from F were they, in terms of x and y, when they met?
(A) 40(x-y)/x+y
(B) 40x-y/x+y
(C) x-y/x+y
(D) 40y/x+y
(E) 40x/x+y
OA is E
Let x = 2 miles per hour (Hayden's rate) and y = 3 miles per hour (Ava's rate).
When people travel TOWARD each other, they WORK TOGETHER to cover the distance between them.
Thus, we ADD their rates.
Combined rate for Hayden and Ava walking toward each other = 2+3 = 5 miles per hour.
Time for Hayden and Ava to travel the 40 miles between them = d/r = 40/5 = 8 hours.
Distance from F = distance traveled by Hayden in 8 hours = r*t = 2*8 = 16 miles. This is our target.
Now we plug x=2 and y=3 into the answers to see which yields our target of 16.
Since x-y = 2-3 = -1, any answer choice that includes x-y can be eliminated.
Eliminate A, B and C.
Answer choice D: 40y/(x+y) = (40*3)/(2+3) = 24.
Doesn't work.
Eliminate D.
The correct answer is
E.
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