Question

A bus travels at a speed of 40 km/hr for 10 min, then at 55 km/hr for 30 minutes and finally at 25 km/hr for 20 minutes. What is the average speed of the bus ?

Answer 1

Given,

Speed (S₁) of the bus for first 10 minutes = 40 km/hr

Speed (S₂) of the bus for next 30 minutes = 55 km/hr

Speed (S₃) of the bus for next 20 minutes = 25 km/hr

To Find,

The average speed of the bus.

Solution,

We can simply solve the given numerical problem by using the following formula,

Distance = Speed × Time

(Here, the time is given in minutes so we need to change into hours, to get the proper S.I. units)

T₁ is 10 minutes = $\frac{10}{60}$ hour = $\frac{1}{6}$ hour

T₁ is 30 minutes = $\frac{30}{60}$ hour = $\frac{1}{2}$ hour

T₁ is 20 minutes = $\frac{20}{60}$ hour = $\frac{1}{3}$ hour

Now, we will calculate the total distance traveled by bus:

⇒ (S₁ × T₁) + (S₂ × T₂) + (S₃ × T₃)

⇒ (40 ×  $\frac{1}{6}$  ) + (55 × $\frac{1}{2}$ ) + (25 × $\frac{1}{3}$ )

⇒ 6.67 + 27.5 + 8.33

⇒ 42.51 km/hr

Now, we will calculate the total time taken by the bus:

⇒ T₁ + T₂ + T₃

⇒ $\frac{1}{6}$ + $\frac{1}{2}$ +  $\frac{1}{3}$

⇒ 1 hour

∴ The average speed of the bus is:

⇒ $\frac{Total distance }{total time}$

⇒$\frac{42.51}{1}$

⇒ 42.51 km/hr

(This will be considered as the final result. As the initial units are in the S.I. system, we have to use the S.I. unit for the final answer too. the S.I. unit of speed is km/hr)

Hence, the average speed of the bus is 42.51 km/hr.