Question

A bus travelling the first one third distance at a speed of 10km/h the next one third at 20km/h and at last one third at 60km/h the average speed of bus is​

Answer 1

Answer:

Average speed of the bus = 18 km/h

Step by step explanations :

Given that,

A bus travelling the first one third distance at a speed of 10km/h

the next one third at 20km/h

and at last one third at 60km/h

1st Method :

let the total distance travelled by bus

be d

so,

time taken to cover d/3 at 10 km/h

= (d/3)/10

= d/30 h

time taken to cover d/3 at 20 km/h

= (d/3)/20

= d/60 h

time taken to cover d/3 at 60 km/h

= (d/3)/60

= d/180 h

now,

Average speed of bus

Average speed of bus = total distance covered/total time taken

total distance covered = d

total time taken = d/30 + d/60 + d/180

(6d + 3d + d) /180

10d/180

= d/18 h

so,

now we have,

distance covered = d

time taken = d/18

so,

Average speed = d/(d/18)

= 18d/d

= 18 km/h

so,

Average speed of the bus

= 18 km/h

________________

2nd Method :

let the 1st speed be V1

2nd speed be V2

and 3rd speed be V3

so,

V1 = 10 km/h

V2 = 20 km/h

V3 = 60 km/h

Average speed

= 3V1V2V3/(V1V2 + V2V3 + V3V1)

putting the values,

3 × 10 × 20 × 60 /(10(20) + 20(60) + 60(10))

30 × 20 × 60/(200 + 1200 + 600)

36000/2000

= 18 km/h

Average speed = 18 km/h

Answer 2

Answer:-

$A_v = 18 km/hr$

Given :-

A bus travelling the first one - third distance at a speed of 10 km/hr.

Next one - third at 20 km /hr

last one - third at 60 km /hr

To find :-

The average speed of bus.

Solution:-

Let the total distance be x km.

Case :- 1

Distance covered = x/3

speed = 10 km/hr

Time taken by bus:-

→$\mathsf{ t = \dfrac{S}{v}}$

→$\mathsf{ t = \dfrac{\dfrac{x}{3}}{10}}$

→$\mathsf{t = \dfrac{x}{30}}$

Case :- 2

Distance covered = x/3

Speed = 20 km /hr

Time taken by bus :-

→$\mathsf{t' = \dfrac{\dfrac{x}{3}}{20}}$

→$\mathsf{ t' = \dfrac{x}{60}}$

Case :- 3

Distance covered = x/3

Speed = 60 km /hr

Time taken by bus :-

→$\mathsf{t" = \dfrac{\dfrac{x}{3}}{60}}$

→$\mathsf{ t" = \dfrac{x}{180}}$

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

Total time taken:-

→$T = t + t' + t"$

→$\mathsf{T = \dfrac{x}{30}+\dfrac{x}{60}+\dfrac{x}{180}}$

→$\mathsf{T = \dfrac{6x +3x + x}{180}}$

→$\mathsf{T = \dfrac{10x}{180}}$

→$\mathsf{ T = \dfrac{x}{18}}$

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

→$\mathsf{A_v = \dfrac{x}{\dfrac{x}{18}}}$

→$\mathsf{A_v = \dfrac{18x}{x}}$

→$\mathsf{A_v = 18 km/hr }$

hence,

Average speed of bus will be 18 km/hr.