Discussion
A covers 5 km with different speeds to reach from point P to point Q. He covers 1 km at the speed of 2 km/h, 1 km at the speed of 3 km/h, 1 km at the speed of 5 km/h, 1 km at the speed of 6 km/h and 1 km at the speed of 10 km/h. He takes a rest for 15 minutes after covering each km. His average speed from point P to point Q is _________ km/h.
Answer: A
The average speed is 2.17 km/h.
The walking times for the five kilometres are 1/2, 1/3, 1/5, 1/6 and 1/10 hours, which add up to 39/30 = 1.3 hours. He rests 15 minutes after each kilometre except at the end, that is four rests, which add 1 hour. The total time is 2.3 hours.
\[ \frac{5}{2.3}\approx2.17 \]
Counting a fifth rest would give 1.96, which is not an option.
Average speed is total distance divided by total time, never the mean of the speeds. The time on the road is 1.3 hours and the rests add 1 hour, so the total is 2.3 hours. The mean of the five speeds, 5.2 km/h, would be wrong.
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