The sports car travels d distance for t time at speed, s, 95 mph until it overtakes the family car. The equation for the sports car is d = 95t
The family car travels the same distance, d, but since it left 4.5 hours earlier than the sports car, it travels for t + 4.5 time until it is overtaken. It travels at speed, 35 mph. The equation for the family car is d = 35(t + 4.5)
We solve the two equations as a system of equations.
d = 95t d = 35(t + 4.5)
Since d = d, set the right sides of the equations above equal to each other.
95t = 35(t + 4.5)
95t = 35t + 157.5
60t = 157.5
t = 2.625
The answer is 2.625 hours, or 2 hours, 37 minutes, and 30 seconds.
Check: In 2.625 hours, the sports car travels: 95 mph * 2.625 h = 249.375 miles The family car traveled 2.625 hours plus the extra 4.5 hours, or 7.125 hours. In 7.125 hours, the family car travels 35 mph * 7.125 h = 249.375 miles. The cars have traveled the same distance 2.625 hours after the sports car left, so our answer is correct.
