A boy leaves on a bicycle trip at the rate of 8 mph One hour

A boy leaves on a bicycle trip at the rate of 8 mph. One hour later the father, realizing that his son forgot his camping gear, sets out by car. How fast must the father drive to overtake the boy in 15 minutes?
D= x
R= 8mph
T= 1hr + 15min.-----> 75min.
8x75min. = 600 mph.

Solution

After the boy has been gone for 1 hour at 8 miles per hour, he will be 8 miles from home. If Dad catches him in 15 minutes, then he will have traveled another 15 minutes at 8 miles per hour. Since 15 minutes is one-quarter hour, he will have gone another 8 divided by 4 = 2 miles. The 8 miles the boy traveled in the first hour plus the 2 miles he traveled in the following 15 minutes makes a total of 10 miles -- and that is the distance Dad has to travel in that 15 minutes. 10 miles per 15 minutes times 4/4 = 40 miles per 60 minutes = 40 miles per hour.