Question

A motorcyclist drives from place A to B with a uniform speed of 30km/h and returns from place B to A with a uniform speed of 20km/h , Find his average speed. ​

Answer 1

Answer:

let the distance be x

while going........

d=xkm

speed=30km/hr

time=d/s=x/30

while coming........

d=x

speed=20km/hr

time=x/20

now,avg speed=total distance /total time

=x+x/x/20+x/30

=2x/5x/60

=2*12

=24km/hr

I hope it helps you

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Answer 2

$\underline{\underline{\huge{\mathfrak{\orange{Given :}}}}}$

• Speed from A to B = 30km/h
• Speed from B to A = 20 km / h

$\underline{\underline{\huge{\mathfrak{\blue{To\ find :}}}}}$

• Average Speed

$\underline{\underline{\huge{\mathfrak{\purple{Solution : }}}}}$

Let the distance between two places A and B be x km .

By the formula of speed

$\boxed{ \large{ \rm \purple{ speed = \frac{distance}{time} }}}$

$\sf \therefore \: \large{time = \frac{distance}{speed} }$

Time taken in first part of journey when speed is 30km/hr is given by

$\sf \: t_1= \dfrac{x \: }{30} hours$

Time taken in second part of journey when speed is 20 km / hr is given by

$\sf t_2 = \dfrac{x}{20} \: hours$

Total time taken in completing the journey is given by

$\sf \implies \: t \: = t_1 + t_2$

$\sf \implies t = \dfrac{x}{30} + \dfrac{x}{20}$

$\sf \implies t = \dfrac{20x + 30x}{600}$

$\sf \implies \: t = \dfrac{50x}{600}$

$\sf \implies t = \dfrac{x}{12} hours$

Using this value of t in the formula of speed

$\sf \orange{average \: speed } = \dfrac{ \red{total \: distance}}{ \green{total \: time} }$

$\rightarrow$Total distance = x + x = 2x km .

$\sf \: average \: speed \: = \dfrac{2x}{ \dfrac{x}{12} }$

$\implies \sf \: average \: speed \: = \dfrac{2x \times 12}{x}$

$\boxed{ \therefore \sf \pink{average \: speed \: = 24kmh^{ - 1}}}$