Answer:
It takes 1.68 hours to catch up to them.
Step-by-step explanation:
The speed of robber = 71 mph
The speed of police = 78 mph
The police start 10 minutes later
by that time robber would have travelled
[tex]distance = \frac{speed}{time}[/tex]
10 minutes =0.166667 hours
then the distance = 11.8 mph
Let them meet at distance x from the bank.
time taken by police to reach x , time =[tex]\frac{ x}{78}[/tex]----------------------(1)
time taken by robber in the same time = [tex]\frac{x-11.8}{71}[/tex]---------------(2)
Equating (1) and (2)
[tex]\frac{x}{78} =\frac{ x-11.8}{71}[/tex]
[tex]71 x = 78(x - 11.8)[/tex]
71x =78x - 920.4
920.4 = 78x - 71x
920.4 = 7x
x = 131.48
The distance where they catch up with the robber from the bank is 131.48 miles
speed of police = 78 mph
distance = 131.48 miles
time they catch up = [tex]\frac{131.48}{78}[/tex]
= 1.68 hours
