Answer: 5 hours
Step-by-step explanation:
Given: The distance between the cities Atlanta and Indianapolis=540 miles
The speed of motorcycle= 48 mph
Since, [tex]Time=\frac{Distance}{speed}[/tex]
[tex]\\\Rightarrow\text{Time taken by motorcycle to travel}=\frac{540}{48}=11.25\ hours[/tex]
Thus, time taken by car to travel the distance= 11.25-2.25= 9 hours
[tex]\\\Rightarrow\text{Speed of car}=\frac{540}{9}=60\ mph[/tex]
Let t be the time at which they will meet if they are moving towards each other simultaneously.
Then Distance covered by Motorcycle+Distance covers by car= 540 miles
[tex]\\\Rightarrow48t+60t=540\\\Rightarrow108t=540\\\Rightarrow\ t=5[/tex]
Thus they will meet in 5 hours, after which time the motorcycle will have traveled [tex]48\times5=240\miles[/tex]
and the car will have traveled [tex]60\times5=300\miles[/tex]
