Answer:
4.5 hours
Step-by-step explanation:
Let x hours be the time needed the motorcycle to catch the car.
Car:
Time [tex]=t+1\dfrac{1}{2}[/tex] hours
Rate = 48 mph
Distance [tex]=48\cdot \left(t+1\dfrac{1}{2}\right)[/tex] miles
Motorcycle:
Time [tex]=t[/tex] hours
Rate = 64 mph
Distance [tex]=64\cdot t[/tex] miles
The distance traveled is the same, so
[tex]48\cdot \left(t+1\dfrac{1}{2}\right)=64\cdot t\\ \\48t+72=64t\\ \\72=16t\\ \\t=4.5\ hours[/tex]
