Two Taps

The scenario is my own, but the idea is a classic:

A bath takes 20 minutes to fill with just the cold tap, or 30 minutes to fill with just the hot tap. How long would it take to fill the bath with both taps together?

It’s possible to get horribly muddled with this problem, but with the right approach a correct answer comes out quite quickly. In 1 hour, the cold tap can fill 3 baths and the hot tap can fill 2 baths, so both taps together can fill 5 baths in 1 hour, or 1 bath in 12 minutes.

This is one of my favourite problems to pose to other people: it is easily understood, and even if they don’t solve it there and then, most will give it at least some thought.

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