Question

A bus covers 128 km in 2 hours and a train covers 240 km in 3 hours. Find the ratio of their speeds.

Answer 1

Hint: In the question, we need to evaluate the ratio of the speed of the bus and the train such that the bus covers 128 km in 2 hours and a train covers 240 km in 3 hours. For this, we will use the relation between the distance, speed and the time travelled by the object.

Complete step-by-step answer:
The relation between the distance travelled by the object with the defined speed in the given time is given as $ Distance = Speed \times Time $ .
According to the question, the bus covers a distance of 128 km in 2 hours.
Let the speed of the bus be $ {v_b} $ .
Substituting the values in the formula $ Distance = Speed \times Time $ to determine the speed of the bus.
 $
  Distance = Speed \times Time \\
   \Rightarrow 128 = {v_b} \times 2 \\
   \Rightarrow {v_b} = \dfrac{{128}}{2} \\
   \Rightarrow {v_b} = 64{\text{ km/hr}} - - - - (i) \;
  $
Again, it has been given that the train covers a distance of 240 km in 3 hours.
Let the speed of the bus be $ {v_t} $ .
Substituting the values in the formula $ Distance = Speed \times Time $ to determine the speed of the train.
 $
  Distance = Speed \times Time \\
   \Rightarrow 240 = {v_t} \times 3 \\
   \Rightarrow {v_t} = \dfrac{{240}}{3} \\
   \Rightarrow {v_t} = 80{\text{ km/hr}} - - - - (ii) \;
  $
As per the demand of the question, we need to find the ratio of the speed of the bus and the train. So, by equations (i) and (ii),
 $
  \dfrac{{{v_b}}}{{{v_t}}} = \dfrac{{64}}{{80}} \\
   = \dfrac{4}{5} \;
  $
Hence, the ratio of the speed of the bus to the train is given as 4:5.
So, the correct answer is “4:5”.

Note: It is worth noting here that the units of the speeds are kilometers per hour in both the cases of the bus and the train and so, there is no need to change the units. However, if the units are different then, it is very essential to change either of the units to one and then, take the ratio of both so as to get the correct result.