A motorcycle breaks down and the rider must walk the rest of

A motorcycle breaks down and the rider must walk the rest of the way to work. The motorcycle was being driven at 45 mph, and the rider walks at a speed of 6 mph. The distance from home to work is 25 mi, and the total time for the trip was 2 hrs. How far did the motorcycle go before it broke down?

Solution

Walking DATA:
distance = x miles ; rate = 6 mph ; time = x/6 hrs
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Motocycle DATA:
rate = 45 mph ; distance = (25-x) mi ; time = (25-x)/45 hrs
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Equation :
time + time = 2 hrs
x/6 + (25-x)/45 = 2
45x + 6(25-x) = 2*6*45
45x + 150 - 6x = 6*90
39x = 540 - 150
39x = 390
x = 10 miles (distance walked)
25-x = 15 miles (distance ridden)