Question

A police officer is chasing a purse-snatcher down a street. The thief

starts 9 meters ahead of the officer and can run 20 meters in 4 second
(5 m/s). The police officer can run 32 meters in 4 seconds (8 m/s). How long will it take the officer to catch the thief?

Answer 1

It would take the police officer about 3 seconds to catch the purse-snatcher.

Answer 2

3 seconds

Step-by-step explanation:

We can give an expression for the position of both the thief and of the police officer at time t.

The position of the thief at time t is given by

`x_t = 9 + 5t`

where 9 is its initial position in m and 5 is its speed in m/s.

Instead, the position of the police officer at time t is given by

`x_o = 0+8t`

where 0 is its initial position in m and 8 is its speed in m/s.

The police officer will catch the thief when their position will be equal, so

`x_t = x_o`

By solving,

`9+5t=8t\\3t=9\\t=3 s`