Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 15 mi, the distance between the cars was 5 mi more than the distance traveled by the car heading east. How far had the eastbound car traveled?

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Answer 1 · 2016-09-02T02:19:07

The eastbound car went $20$ miles.

Draw a diagram, letting $x$ be the distance covered by the car travelling eastbound.

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By pythagorean theorem (since the directions east and north make a right angle) we have:

$15^2 + x^2 = (x+ 5)^2$

$225 + x^2 = x^2 + 10x+ 25$

$225 - 25 = 10x$

$200 = 10x$

$x = 20$

Hence, the eastbound car has travelled $20$ miles.

Hopefully this helps!