JAMB 1987 · UME · Q5

Commercial arithmetic

A train moves from $P$ to $Q$ at an average speed of 90 km/h and immediately returns from $Q$ to $P$ along the same route at an average speed of 45 km/h. Find the average speed for the entire journey.

Worked solution (try it first)

Let each way be $d$ km.
Time is distance over speed, so the total time is $\dfrac{d}{90} + \dfrac{d}{45} = \dfrac{d + 2d}{90}$
$= \dfrac{d}{30}$ hours.
Average speed is total distance over total time: $2d \div \dfrac{d}{30} = 60$ .
So the average speed is 60.00 km/h, option B.

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