Question

A train is moving at a uniform speed of $75$ km/hour.
(i) How far will it travel in $20$ minutes?
(ii) Find the time required to cover a distance of $250$ km.
[4 marks]

Answer 1

Let the distance travelled (in km) in $20$ minutes be $x$ and time taken (in minutes) to cover $250$ km be $y$.

Distance travelled (in km)	$75$	$x$	$250$
Time taken (in minutes)	$60$	$20$	$y$

Since the speed is uniform, therefore, the distance covered would be directly proportional to time.
$\Rightarrow \frac{D}{T}=constant$
$\Rightarrow \frac{D_1}{T_1}=\frac{D_2}{T_2}$

[1 mark]

(i) Distance travelled in $20$ minutes :
$\Rightarrow \frac{75}{60}=\frac{x}{20}$
$\Rightarrow x=\frac{75\times 20}{60}=25$ km

Thus, the train will cover a distance of $25$ km in $20$ minutes.

[1.5 marks]

(ii) Time required to cover a distance of $250$ km:
$\Rightarrow \frac{75}{60}=\frac{250}{y}$
$\Rightarrow y=\frac{250\times 60}{75}=200$ minutes

Thus, a distance of $250$ kilometres will be covered in $200$ minutes.

[1.5 marks]