Question

A motorcyclist drivers from 'A' to 'B' with a uniform speed of 30 km/h and returns back with a speed of 20 km/h . Find its average speed.
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Answer 1

Answer:

Explanation:

Given :-

Speed of motorcycle from A to B = 30 km/h

Speed of motorcycle from B to A = 20 km/h

To Find :-

Average Speed = ??

Formula to be used :-

Average Speed = Total distance covered/Total time taken

Solution :-

Let the distance covered is x.

Total distance covered = x + x = 2x

Time taken from A to B = x/30

Time taken from B to A = x/20

Total time taken, t = x/30 + x/20 = 5x/60

Now, Average Speed = Total distance covered/Total time taken

⇒ Average Speed = 2x × 60/5x

⇒ Average Speed = 24 km/h

Hence, the Average Speed is 24 km/h.

Answer 2

Given :-

Motorcyclist cover distance from A to B with a speed of 30km/h

Returns back with a speed of 20km/h

Distance remains same. !

To find :-

★ Average speed of motor cyclists

Now find the time taken to go from A to B

Let the distance be n

$\sf \ speed = \dfrac{Distance }{Time }\\ \\ :\implies\sf Time_1 = \dfrac{Distance_1}{speed_1}\\ \\ :\implies\sf Time_1 = \dfrac{n}{30}$

Now time taken In returning back

Distance remains same n

$\sf :\implies\sf Time_2 = \dfrac{Distance_2}{speed_2}\\ \\ :\implies\sf Time_1 = \dfrac{n}{20}$

Now find the average speed of motorcyclist !

$\boxed{\sf\ \ Average \ speed = \dfrac{Total\ Distance}{Total \ time }}$

$:\implies\sf Av. \ speed = \dfrac{d_1+d_2}{t_1+t_2}\\ \\ :\implies\sf Av.\ speed = \dfrac{n+n}{\dfrac{n}{30}+ \dfrac{n}{20}}\\ \\ :\implies\sf Av.\ speed = \dfrac{2n}{\dfrac{2n+3n}{60}}\\ \\ :\implies\sf Av.\ speed = 2 \cancel{n} \times \dfrac{60}{5\cancel{n}}\\ \\ :\implies\sf Av. \ speed = \dfrac{\cancel{60}\times 2}{\cancel5}\\ \\ :\implies \sf Av. \ speed = 12\times 2 = 24 km/h$

$\underline{\bigstar{\sf \ Average \ speed = 24km/h}}$