Question

Bank robber holds up a bank and speeds off at 71 mph. Police start chasing him 10 minutes later going 78 mph. How long will it take to catch up to them?

Answer 1

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

$distance = \frac{speed}{time}$

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 =$\frac{ x}{78}$----------------------(1)

time taken by robber in the same time = $\frac{x-11.8}{71}$---------------(2)

Equating (1) and (2)

$\frac{x}{78} =\frac{ x-11.8}{71}$

$71 x = 78(x - 11.8)$

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 = $\frac{131.48}{78}$

= 1.68 hours