Dear Uncle Colin,

I have a question I can’t make sense of: “It takes 3 bricklayers four hours to lay 4200 bricks. How long would it take 2 bricklayers to lay 3150 bricks?” I can never figure out when to multiply and when to divide!

Markscheme Obtusely Recommends Taking A Ratio

Hi, MORTAR, and thank you for your message!

My key trick to working out when to divide and when to multiply is to ask: *would changing this number make the workers lay more bricks or fewer?”

Thinking it through (1)

For instance, with this one, we know that three bricklayers lay 4200 bricks in four hours. What happens if we only have two bricklayers, but keep the time the same? We lay fewer bricks, two-thirds as many. That’s 2800 bricks.

But we want 3150 bricks. That will take the two builders longer - by a factor of $\frac{3150}{2800} = \frac{9}{8}$. Nine-eights of four hours is four and a half hours, which is the answer.

Thinking it through (2)

Depending on how happy you are with the fractions, that might be a bit much, so here’s another method: take things down to ones. One bricklayer, one hour. Then see where you are.

If 3 bricklayers take four hours to lay 4200 bricks, one bricklayer takes four hours to lay 1400. They would take one hour to lay 350 bricks.

That means, two bricklayers lay 700 bricks in an hour.

How many hours do they take to lay 3150? Well, it’s certainly more than one - if you’ve got your estimating hat on, it’s between 4 and 5. If you then work out 3150 divided by 700, it give you four and a half hours again.

I hope that helps!

- Uncle Colin