Question

52. A man covers a journey from place A to place B at the speed of 51kmph and returns at the speed of 57kmph. Find the average speed. a) 26.92kmph b) 54kmph c) 55kmph d)53.83kmph​

Answer 1

Answer:

Option D

Step-by-step explanation:

Given :-

A man covers a journey from place A to place B at the speed of 51kmph and returns at the speed of 57kmph

To Find :-

Average speed

Solution :-

Let the distance from A to B be S

Now we know that

Time = Distance/Speed

From A to B

=> Time = S/51

From B to A

=> Time = S/57

Now

Average speed = Total distance covered/Total time

=> S + S/(S/51 + S/57)

=> 2S/(19S + 17S/969)

=> 2S/(36S/969)

=> 2S/(12S/323)

=> 2S × 323/12S

=> 323/6

=> 53.83 km/h

Option D

Answer 2

Answer:

53.83 km/h

Step-by-step explanation:

A man covers a journey from place A to place B at the speed of 51kmph and returns at the speed of 57kmph.

Here, the distance of the journey, from A to B and from B to A are same.

When same distance is covered in two different speeds, v₁ and v₂, Average speed is given as:

$\big{v_{d,avg} = \frac{2v_1v_2}{v_1+v_2}}$

$\text{So, Average speed = } v_{d,avg} \\ \\ = \frac{2v_1v_2}{v_1+v_2}\\ \\ = \frac{2 \times 51 \times 57}{51+57} \\ \\ =\boxed{53.83 \text{ km/h}}$

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Note: When an object moves at two different speeds, v₁ and v₂ for equal amount of time t, Average speed is given as:  (v₁ + v₂)/2.

In the question, distance travelled is same. In the note, the time of travel is same.

Similar concept : https://brainly.in/question/46083965