Working together

Hello, and welcome to Myriora Maths! Tap A fills a bath in six minutes. Tap B fills it in three minutes. If both taps are on, how long does it take?

Here's the trick: give the bath a size. We don't know how big it is, so we choose! Pick a number that six and three both go into: six works. So the bath holds six buckets.

Tap A fills six buckets in six minutes: that's one bucket a minute. Tap B fills six buckets in three minutes: that's two buckets a minute.

Together, they fill one plus two: three buckets every minute. After one minute, three buckets. After two minutes, six buckets: the bath is full! So it takes two minutes.

Why can't we just add the times? Two taps make the job quicker, not slower. What adds up is the work done each minute. That's why we count buckets a minute.

Let's try another. Ann paints a fence in four hours. Ben takes twelve hours. Pick a size: twelve panels. Ann paints three panels an hour, and Ben paints one. Together, that's four panels an hour. So twelve panels take three hours.

A common mistake is adding the times: six plus three is nine minutes. But that's slower than tap B on its own! With both taps on, it must be quicker than three minutes. The answer is two minutes.

Your turn! Tap A fills a tank in ten minutes. Tap B fills it in fifteen minutes. With both taps on, how long does it take? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Pick a size that ten and fifteen both go into: thirty buckets. Tap A fills three a minute, and tap B fills two. Together, that's five a minute. Every minute, five more buckets go in. Thirty buckets take six minutes!

Quick review. Give the job a size that all the times go into. Work out how much each one does in a minute. Add those up, then divide the size by the total. See you next time!