Average Speed Over Both Journeys

This question is sometimes asked on the GMAT exam, allegedly.

A woman drives to work every morning at an average speed of 30kmph. In the evening, she drives home the same distance at an average speed of 40kmph. What is her average speed over both journeys?

HINT: The answer isn't 35kmph!

The answer isn't 35kmph because if the woman took an hour to drive to work in the morning, she would cover a distance of 30km. And if she drove for an hour to get back home in the evening, she'd clock up 40km. But the distance to and from work is the same, so it couldn't have taken her the same amount of time to complete both journeys.

We weren't given the distance to/from work, but let's suppose it's the least common multiple of 30 and 40 which is 120. In which case, the woman would take 4 hours to drive to work in the morning and 3 to return home in the evening, covering a distance of 240km in all.

So her average speed over both journeys is 240 / 7 or 34 27kmph.

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