Question

A thief is spotted by a policeman from a distance of \[100{\text{ }}metres\] . When the policeman starts the chase the thief also starts running. If the speed of the thief is 8km/hr than that of the policeman \[10km/hr\] , how far the thief will have to run before he is overtaken?
A. \[300{\text{ }}m\]
B.\[350{\text{ }}m\]
C.\[400{\text{ }}m\]
D.\[450{\text{ }}m\]

Answer 1

Hint: Firstly find the change in the speed of both thief and policeman. Then calculate the time taken for the police to catch the thief and at last calculate the distance between the policemen and thief.

Complete step-by-step answer:
\[1{\text{ }}km{\text{ }} = {\text{ }}1000{\text{ }}m\]
Since distance is 100 metres and speed is given in km/hr so we have to convert distance into km.
Distance is $ \dfrac{{100}}{{1000}} = \;0.1{\text{ }}km $
Let's assume
Time = x
Speed of policeman = distance + speed of thief
\[
\Rightarrow {10x{\text{ }} = \;0.1{\text{ }} + {\text{ }}8x} \\
\Rightarrow {10x{\text{ }}-{\text{ }}8x{\text{ }} = {\text{ }}0.1} \\
\Rightarrow {2x{\text{ }} = {\text{ }}0.1} \\
\Rightarrow {x = 0.05}
\]
So time taken by the policeman is \[0.05{\text{ }}hours\] to catch the thief .
Thief have to run
\[\left( {.05} \right) \times \left( 8 \right){\text{ }} = {\text{ }}0.4km{\text{ }} = {\text{ }}400{\text{ }}metres\]

Note: Revise all the concepts of distance, time and speed. Also revise that the relative speed of two objects moving in the same direction is the change in speed of both the objects and if they are moving in the same direction the relative speed becomes the sum of speed of both the objects.