Question

O to
With
3o. A motorcyclist dosives from place
a uniform speed of
8o 30 km/h and botuons from place
B bo with a uniform speed
of 20km hl . Find his are tage
speed​

Answer 1

Answer:

$\boxed{\mathfrak{Average \: speed \ (v_{avg}) = 24 \: km/h}}$

Given:

Uniform speed with which motorcyclist drive from A to B = 30 km/h

Uniform speed with which motorcyclist drive from B to A = 20 km/h

To find:

Average speed of motorcyclist ($\rm v_{avg}$)

Explanation:

Let distance between A to B be 'd'

So, Total distance travelled by motorcyclist = 2d

Let the time taken to travel from A to B be $\rm t_{1}$

As we know;

$\rm speed = \dfrac{distance}{time}$

$\therefore$

$\rm \implies 30 = \dfrac{d}{t_{1}} \\ \\ \rm \implies t_{1} = \dfrac{d}{30}$

Let the time taken to travel from B to A be $\rm t_{2}$

$\therefore$

$\rm \implies 20 = \dfrac{d}{ t_{2}} \\ \\ \rm \implies t_{2} = \dfrac{d}{20}$

Total time for covering 2d distance (t) = $\rm t_{1} + t_{2}$

$\boxed{\bold{Average \: speed \ (v_{avg})= \frac{Total \: distance \ travelled}{Total \: time \ taken}}}$

By substituting values we get:

$\rm \implies v_{avg} = \dfrac{2d}{t} \\ \\ \rm \implies v_{avg} = \dfrac{2d}{t_{1} + t_{2}} \\ \\ \rm \implies v_{avg} = \dfrac{2d}{ \dfrac{d}{30} + \dfrac{d}{20} } \\ \\ \rm \implies v_{avg} = \dfrac{2d}{ \dfrac{2d}{60} + \dfrac{3d}{60} } \\ \\ \rm \implies v_{avg} = \dfrac{2d}{ \dfrac{2d + 3d}{60} } \\ \\ \rm \implies v_{avg} = \dfrac{2d}{ \dfrac{5d}{60} } \\ \\ \rm \implies v_{avg} = \dfrac{2 \cancel{d} \times 60}{5 \cancel{d}} \\ \\ \rm \implies v_{avg} = \dfrac{2 \times 60}{5} \\ \\ \rm \implies v_{avg} = \dfrac{120}{5} \\ \\ \rm \implies v_{avg} = 24 \: km/h$

Answer 2

$\huge\mathcal{QUESTION:-}$

✨✨ A motorcyclist drives from A to B with a uniform speed of 30 km/h and returns with a speed of 20 km/h . Find the average speed .

$\huge\mathcal{ANSWER:-}$

$\bf{\gray{\underbrace{\blue{GIVEN:-}}}}$

• A motorcyclist drives from A to B with a uniform speed of 30 km/h .

• It returns with a speed of 20 km/h .

$\bf{\gray{\underbrace{\blue{TO\: FIND:-}}}}$

• The average speed .

$\bf{\gray{\underbrace{\blue{SOLUTION:-}}}}$

Let,

• The distance between A to B is “ X m ” .

$\orange\bigstar\:\bf{\pink{\overbrace{\underbrace{\purple{Time\:=\:\dfrac{Distance}{Speed}\:}}}}}$

$\bf{\implies\:Total\:time\:=\:t_1\:+\:t_2\:}$

$\rm{\implies\:Total\:time\:=\:\dfrac{X}{30}\:+\:\dfrac{X}{20}\:}$

$\rm\green{\implies\:Total\:time\:=\:\dfrac{5X}{60}h\:}$

$\green\bigstar\:\bf{\pink{\overbrace{\underbrace{\purple{Average\:Speed\:=\:\dfrac{Total\:Distance}{Total\:Time}\:}}}}}$

• Total distance = 2X km

• Total time = 5X/60 h

$\rm{\implies\:Average\:speed\:=\:\dfrac{2X}{5X/60}\:}$

$\rm{\implies\:Average\:speed\:=\:\dfrac{2X}{5X}\times{60}\:}$

$\rm{\implies\:Average\:speed\:=\:2\times{12}\:}$

$\bf\red{\implies\:Average\:speed\:=\:24\:km/h\:}$

$\rm\pink{\therefore}$ The average speed of the motorcycle is “24 km/h” .