Question

A boy runs for 10 min at a uniform speed of 9 km/h. At what speed should he run for the next 20 min so that the average speed comes to 12 km/h?

Answer 1

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The boy runs 10 min or 10/60 = 1/6 h at uniform speed 9 km/h.

Distance he travels in 1/6 h is = 9 × (1/6) = 1.5 km

Then he runs 20 min or 20/60 = 1/3 h at uniform speed, say, v.

Distance he covers in this 1/3 h is = v/3 km

So, total distance covered = 1.5 + v/3

Total time taken = 1/6 + 1/3 = 0.5 h

Now, average speed = total distance/total time

=> 12 = (1.5 + v/3)/0.5

=> v = 13.5 km/h

So, the boy has to travel at speed 13.5 km/h for 20 min.