Question

A bus travelled with speed 40km/h half the distance and remaining half distance with speed of 60km/h find the average speed

Answer 1

Answer:-

$\mathsf{ A_v = 48 km/hr}$

Given :-

A bus travelled half distance with speed of 40 km/hr.

And remaining half distance with speed of 60 km/hr.

To find :-

Average speed of bus.

Solution:-

Let the total distance be x km.

• Half distance is covered with speed 40 km/hr.

→$\mathsf{ S_1 = \dfrac{x}{2}}$

v = 40 km/hr

Time taken by bus :-

$\mathsf{S_1 = vt}$

→$\mathsf{\dfrac{x}{2} = 40 \times t}$

→$\mathsf{t = \dfrac{\dfrac{x}{2}}{40}}$

→$\mathsf{t = \dfrac{x}{80}}$

• Remaining half distance with speed of 60 km/hr.

→$\mathsf{S_2 = \dfrac{x}{2}}$

v = 60 km/hr

→$\mathsf{t = \dfrac{\dfrac{x}{2}}{60}}$

→$\mathsf{ t = \dfrac{x}{120}}$

Average speed → It is the ratio of the total distance travelled by body to total time taken during whole journey.

→$\mathsf{ A_v = \dfrac{\text{Total distance travelled}}{\text{Total time taken}}}$

Total distance travelled = x km

Total time taken :-

→$\mathsf{T = \dfrac{x}{80}+\dfrac{x}{120}}$

→$\mathsf{ T = \dfrac{3x+2x}{240}}$

→$\mathsf{T = \dfrac{5x}{240}}$

• Put the values,

→$\mathsf{A_v = \dfrac{x}{\dfrac{5x}{240}}}$

→$\mathsf{A_v = \dfrac{240x}{5x}}$

→$\mathsf{A_v = 48 km/hr }$

hence,

Average speed of bus is 48 km/hr.