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!