A car trip from New York to Cincinnati took 12.5 hours. The return trip by the same route took 1 hour longer because the average rate of speed was 4 mph less. What is the length of the route?

A car trip from New York to Cincinnati took 12.5 hours. The return trip by the same route took 1 hour longer.

Let x be the speed of the car

Car trip from New York to Cincinnati

We know Distance D = speed * time

time = 12.5 hours and speed = x

D = 12.5x

Return trip

The return trip by the same route took 1 hour longer. So 12.5+1 = 13.5 hours

he average rate of speed was 4 mph less. So speed is x-4

Distance D = speed * time

time = 13.5 hours and speed = x-4

D = (x-4) * 13.5

D = 13.5x-54

The distance of ongoing trip and return trip are same

So we equate both the distance equations D = 13.5x-54 and D = 12.5x

12.5x = 13.5x-54

Subtract 13.5 on both sides

-1x = - 54

x=54

speed of ongoing trip = 54 miles per hour

Distance D = 12.5x = 12.5 * 54=675 miles

The length of the route = 675 miles