The family car leaves the house 1 1/2
hours after the moving van and follows the same route. The moving van travels at an average speed of 45 miles per hour. The family car travels at an average speed of 60 miles per hour. After how many hours of driving will the family car catch up to the moving van?
Let t be the time it takes for the family car to catch up to the moving van.
The moving van has a head start of 45 * 1 1/2 = 67.5 miles.
The distance the family car needs to travel to catch up to the moving van is 67.5 miles.
Since the family car travels at a speed of 60 miles per hour and the moving van travels at a speed of 45 miles per hour, the family car gains on the moving van at a rate of 60 - 45 = 15 miles per hour.
Therefore, we can set up the equation:
15t = 67.5
Solving for t, we get:
t = 67.5 / 15
t = 4.5
After 4.5 hours of driving, the family car will catch up to the moving van.