Question

16.An object travels from A to B with a uniform speed of 30 km/hr and returns back with a speed of 20 km/hr. What will be its average speed ?


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Answer 1

Solution :

Let the distance travelled by object be x

i) While travelling from A to B, average speed is 30 km/hr,Let time taken be $\sf\:t_{1}$

★ Speed = $\sf\dfrac{Distance}{Time}$

→ 30 = $\sf\dfrac{x}{t}_{1}$

→ $\sf\: t_{1} = \dfrac{x}{30}$

ii) While returning from B to A, average speed is 20 km/hr,Let time taken be $\sf\:t_{2}$

★ Speed = $\sf\dfrac{Distance}{Time}$

→ 20 = $\sf\dfrac{x}{t}_{2}$

→ $\sf\: t_{2} = \dfrac{x}{20}$

And now we will consider the whole distance (going from A to B to returning from B to A)

★ Total Distance = x + x = 2x km

★ Total Time taken = $\sf\t_{1}\: +\: t_{2}$

→ $\sf\: \dfrac{x}{30}\: + \dfrac{x}{20}$

→ $\sf\dfrac{3x + 2x}{60}$

→ $\sf\cancel\dfrac{5x}{60}$

→ $\sf\dfrac{x}{12}$

★ Average Speed = Total distance covered/ Total time taken

→ $\sf\dfrac{2x\: \times 12}{x}$

→ 24 km/h

$\therefore$ Average Speed of the object is 24 km/hr.

Answer 2

Given that:

• An object travels from A to B with speed 30 km/hr.

• The same object travels from B to A with speed 20 km/hr.

To Find:

• Average speed of the object.

Formula Used:

• Average speed = total distance/total time

Solution:

Let the distance between A and B be x km.

So, time taken from A to B = x/30 hr.....(1)

Also, time taken from B to A = x/20 hr....(2)

Total distance = x+x = 2x....(3)

Using the above formula, we have

average speed = (3)/[(2)+(1)]

Average speed = 2x/x(1/30+1/20)

Average speed = 2/(5/60)

Average speed = 2*12 = 24 km/hr.

So, the average speed of object is 24 km/hr.

Hope this helps