A car covers the first half of the distance between two places at $40 k m p h$ and the other half at $60 k m p h$ . The average speed of the car is :

40 k m p h

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48 k m p h

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50 k m p h

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60 k m p h

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Solution

The correct option is B $48 k m p h$
Given,

$v_{1} = 40 k m p h$

$v_{2} = 60 k m p h$

Lets consider $d =$ total distance

The time taken to compete half distance with speed $v_{1}$ ,

$t_{1} = \frac{d}{2 v_{1}}$

The time take to complete second half distance with speed $v_{2}$

$t_{2} = \frac{d}{2 v_{2}}$

Total time, $t = t_{1} + t_{2}$

$t = \frac{d}{2 v_{1}} + \frac{d}{2 v_{2}}$

$t = \frac{d}{2} (\frac{1}{v_{1}} + \frac{1}{v_{2}}) = \frac{d (v_{1} + v_{2})}{2 v_{1} v_{2}}$ . . . . . . . . .(1)

The average speed of the car is given,

$v_{a v g} = \frac{d}{t}$

$v_{a v g} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$ (from equation 1)

$v_{a v g} = \frac{2 \times 40 \times 60}{40 + 60} = 48 k m p h$

The correct option is B.

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A car covers the first half of the distance between two places at 40kmph and the other half at 60kmph. The average speed of the car is :

A car covers the first half of the distance between two places at $40 k m p h$ and the other half at $60 k m p h$ . The average speed of the car is :