Mathematics: 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?

Bank robber holds up a bank and speeds off at 71

saykblahwah309

17.01.2022

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

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