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