Question

A bus travels $180km$ in $3$ hours and a train travels $450km$ in $5$ hours. Find the ratio of speed of train to speed of bus.

Answer 1

Find speed of bus and train

Given,

Distance travelled by the bus = $180km$
Time taken by the bus to cover the given distance $=3$ hours

Distance travelled by the bus $=450km$
Time taken by the bus to cover the given distance $=5$ hours

We know that,

Speed $=\frac{\text{distance travelled}}{\text{Time taken}}$

Thus,

Speed of Bus $=\frac{180km}{3hours}=60km/hr$

And,

Speed of Train $=\frac{450km}{5hrs}=90km/hr$

Ratio of speed of train to speed of bus

$=\frac{\text{Speed of train}}{\text{Speed of bus}}=\frac{90}{60}=\frac{9}{6}$

Now, further simplifying the above ratio or fraction into its lowest form by dividing the numerator and denominator by $3$, we get

$\frac{9}{6}=\frac{9÷3}{6÷3}=\frac{3}{2}=3:2$

Therefore, the ratio of the speed of the train to the speed of the bus is $3:2$.