Suppose that Car A can travel 250 miles in 3 hours less time

Suppose that Car A can travel 250 miles in 3 hours less time than it takes Car B to travel 440 miles. The rate of Car B is 5 miles per hour faster than that of Car A. Find the rates of both cars.

Solution

time = distance / rate

(250 / A) + 3 = 440 / (A + 5)

multiplying by A(A + 5) ___ 250A + 1250 + 3A^2 + 15A = 440A

3A^2 - 175A + 1250 = 0

factoring ___ (3A - 25)(A - 50) = 0

3A - 25 = 0 ___ A = 25/3 ___ B = 40/3

A - 50 = 0 ___ A = 50 ___ B = 55