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?

Sep 2, 2016

The eastbound car went $20$ miles.

Explanation:

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

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

${15}^{2} + {x}^{2} = {\left(x + 5\right)}^{2}$

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

$225 - 25 = 10 x$

$200 = 10 x$

$x = 20$

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

Hopefully this helps!