Meeting and chasing

Hello, and welcome to Myriora Maths! Amy and Ben are thirty kilometres apart. They walk towards each other. Amy walks four kilometres an hour, and Ben walks six. When do they meet?

Watch the gap between them. In one hour, Amy walks four kilometres and Ben walks six. So the gap shrinks by ten kilometres: from thirty to twenty. After two hours, it's ten. After three hours, it's zero: they meet!

Walking towards each other, the gap closes by both speeds added together. Four plus six is ten kilometres an hour. Thirty divided by ten is three hours.

Where do they meet? Amy walks for three hours at four kilometres an hour: twelve kilometres. Ben walks for three hours at six: eighteen kilometres. Twelve plus eighteen is thirty. It checks out!

Now a chase. Sam sets off walking at four kilometres an hour. When he's six kilometres ahead, his sister Zoe follows on a bike, at ten kilometres an hour. When does she catch him?

This time they go the same way. Each hour, she rides ten kilometres, but Sam walks four kilometres further on. So she gains only ten minus four: six kilometres an hour. The gap is six kilometres, so she catches him in one hour.

A common mistake is always adding the speeds. In the chase, that gives ten plus four: fourteen kilometres an hour. But Sam is moving away from her, not coming closer! Going the same way, take the speeds away. Going towards each other, add them.

Your turn! Two trains are two hundred and forty kilometres apart. They drive towards each other, at seventy and fifty kilometres an hour. How long until they meet? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! They go towards each other, so add the speeds. Seventy plus fifty is one hundred and twenty kilometres an hour, and two hundred and forty divided by one hundred and twenty is two. They meet after two hours!

Quick review. Find the gap between them. Towards each other, add the speeds. Going the same way, take the smaller speed from the bigger. Then divide the gap by that speed. See you next time!