A bus driver follows a morning route and an afternoon route

A bus driver follows a morning route and an afternoon route each day. Because there are more cities on the morning route, the average speed is 12 miles per hour less than the afternoon route. She covers 70 miles on the morning route in the same amount of time as she covers 100 miles on the afternoon route. Find her average speed on the afternoon route.

Solution

Let the average speed on the morning route be x. Then the average speed on the afternoon route is x + 12. . Since time = distance/ speed , and since the time takenin the morning route to cover 70 miles is the same as the time taken in the afternoon route to cover 100 miles, we have 70/x = 100/ (x + 12) or, 70(x + 12) = 100x or, 70x + 840 = 100x or, 30x = 840 or, x = 840/30 = 28. Thus, the average speed on the morning route is 28 mph and the average speed on the afternoon route is 28+ 12 = 40 mph