Question 32

On a journey across Kolkata, a taxi averages 40 kmph for 60% of distance, 30 kmph for 20% of the distance, and 10 kmph for the remainder. The average speed of the whole journey is

Solution

Let the total distance covered by the taxi be 100 kms.

For 60% of the distance, i.e. 60 Kms, Speed of the taxi was 40 kmph. Time taken to cover 60 kms= $$\ \frac{\ Dis\tan ce}{Speed}\ =\ \frac{\ 60}{40}=\ \frac{\ 3}{2}\ hrs.$$

For 20% of the distance, i.e. 20 Kms, Speed of the taxi was 30 kmph. Time taken to cover 20 kms= $$\ \frac{\ Dis\tan ce}{Speed}\ =\ \frac{\ 20}{30}=\ \frac{\ 2}{3}\ hrs.$$

For remaining, i.e. 20% of the distance, i.e. 20 Kms, Speed of the taxi was 10 kmph. Time taken to cover 20 kms= $$\ \frac{\ Dis\tan ce}{Speed}\ =\ \frac{\ 20}{10}=\ \ 2\ hrs.$$

So, total distance= 100 kms.

Total time= $$\ \ \frac{\ 3}{2}+\ \frac{\ 2}{3}+2=\ \frac{\ 9+4+12}{6}=\ \frac{25\ }{6}hrs$$

.'. Average speed= $$\ \ \ \frac{\ Total\ Dis\tan ce}{Total\ Time}=\ \frac{\ 100}{\ \frac{\ 25}{6}}=\ \frac{\ 100\cdot6}{25}=4\times\ 6=24\ kmph$$

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