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Abdul while driving to school computes the average speed for his trip to be $20 km / h$ . On his return trip along the same route, there is less traffic and the average speed is $40 km / h$ . The average speed for Abdul’s trip is?

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25.82 km / h

26.67 km / h

27.71 km / h

26.12 km / h

answer is B.

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Detailed Solution

The average speed for Abdul’s trip is

26.67 km / h

Given:
Speed while going to school,

v_{1} = 20 km / h

speed while returning,

v_{2} = 40 km / h

we know

average speed (v_{av}) = \frac{Total distances}{Total time taken}

Let the distance of Abdul’s school be

= s

Time taken to his trip to school,

t_{1} = \frac{s}{v_{1}}

, where

v_{1}

is the average speed for his trip while
driving to school.
Time taken, on his return trip,

t_{2} = \frac{s}{v_{2}}

,where

v_{2}

is the average speed for his return trip.

\Rightarrow = \frac{s + s}{t_{1} + t_{2}}

\Rightarrow = \frac{2 s}{\frac{s}{v_{1}} + \frac{s}{v_{2}}}

\Rightarrow = \frac{2 s}{\frac{s (v_{2} + {v_{2})}_{}}{v_{1} v_{2}}}

\Rightarrow

= \frac{2 v_{1} v_{2}}{v_{2} + {v_{2})}_{}}

\Rightarrow

v_{av} = \frac{2 \times 20 \times 40}{20 + 40}

\Rightarrow

= 26.67 km / h

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