Question

Q.14) A motor passes the distance between two villages with the speed 60 km/hr and
returns with the speed 40 km/hr. What is the average speed of that motor through
the entire travel .
EXPLAIN STEP BY STEP​

Answer 1

Given :-

• Travelling speed = 60 km/h
• Returning speed = 40 km/h

To find :-

• Average speed = ?

Solution :-

Using the formula

Average speed = 2v1v2/V1 + V2

Where

• V1 = 60 km/h
• V2 = 40 km/h

Substituting the known values we have

→ Avg speed = 2(60)(40)/60 + 40

→ Avg speed = 4800/100

→ Average speed = 48 km/h

Hence, average speed of motor through entire village = 48 km/h

Answer 2

Answer

Given -

$\bf V_1 = 60 km/hr$

$\bf V_2 = 40 km/hr$

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To find

Average Speed.

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Formula Used -

$\bf V_{avg} = \frac{2v_1v_2}{v_1 + v_2}$

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Derivation -

As the motor goes to the village and returns with the same path , so the distance travelled is the same.

Time taken =

$\bf t_1 = \frac{s}{v_1}$

$\bf t_2 = \frac{s}{v_2}$

Average speed = Total distance/Total time

$\bf v_{avg} = \frac{s + s}{t_1 + t_2}$

$\bf v_{avg} = \frac{2s}{ \frac{s}{v_1} + \frac{s}{v_2} }$

$\bf v_{avg} = \frac{2v_1v_2}{v_1 + v_2}$

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Solution -

$\bf v_1 = 60 km/hr$

$\bf v_2 = 40 km/hr$

Substituting the value in formula -

$\bf v_{avg} = \frac{2v_1v_2}{v_1 + v_2}$

$\bf v_{avg} = \frac{2 \times 60 \times 40}{60 + 40}$

$\bf = \cancel \frac{4800}{100}$

$\bf = 48 km/hr$

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Thanks