Question

A farmer drives a tractor from one town to another, a distance of 120 kilometers. He drives 10 kilometers per hour fast on the return trip, cutting an hour off the time. How fast does he drive each way?

Answer 1

120/x - 120/(x+10) = 1
120x + 1200 - 120x = x(x+10)
1200 = x^2+10x
x^2 + 10x - 1200 = 0
(x+40)(x-30) = 0
Positive solution:
x = 30 km/hr (rate on the 1st trip)
x+10 = 40 km/hr (rate on the return trip)