Mr. Lewis made a round trip between two cities that are 200 km apart. On the return trip, he increased the average rate of travel by 5 km/h and made the trip in 2 hours less time. Find his rate of travel for each direction.
rate * time = distance
distance/rate = time
d = 200
x = original rate
200/x = 200/(x+5) + 2 solve for x
200 (x+5) = 200 x + 2x (x+5)
200x + 1000 = 200x + 2x^2 + 10x
2x^2 +10x -1000 = 0 Use quadratic Formula x = 20 km/hr or -25 (throw out) Faster speed = 20 + 5 = 25 km/hr
200/20 = 10 hours 200/25 = 8 hours Check !