Car A and Car B get on the freeway at the same time and the same point. They are traveling at different speeds, but each car is maintaining its own consistent speed. After a few minutes, Car A is at mile marker 10 and Car B is at mile marker 17. When Car B reaches mile marker 85, at which mile marker is Car A? *

Question

02-07-2017
Mathematics

contestada

Car A and Car B get on the freeway at the same time and the same point. They are traveling at different speeds, but each car is maintaining its own consistent speed. After a few minutes, Car A is at mile marker 10 and Car B is at mile marker 17. When Car B reaches mile marker 85, at which mile marker is Car A? *

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Аноним Аноним · Answer 1 · 2017-07-10T14:13:11+02:00

Let vA = constant speed of car A, mph.
Let vB = constant speed of car B, mph.

After time t hours, car A reaches mile marker 10, so the time taken is
t = 10/vA.
At the same instant, car B reaches the mile marker 17, therefore
t = 17/vB = 10/vA
That is,
vA/vB = 10/17.

When car B reaches the mile marker 85, the time taken is
T = 85/vB.
At the same time, car A reaches the mile marker given by
x = T*vA = (85/vB)*vA = (vA/vB)*85.
Because vA/vB = 10/17, therefore
x = (10/17)*85 = 50.

When car B reaches the mile marker 85, car A reaches the mile marker 50.

Answer: 50