It takes 12 builders eight hours to build a concrete wall. After six hours, two of the builders have to go home. The rest of the builders carry on working until the wall is complete. Assuming that all of the builders work at the same rate, how many extra hours does each of the remaining 10 builders have to work to finish the wall?
There’s a key assumption within this question that allows us to carry out the calculations that we’re going to to solve the problem. And that assumption is that all of the builders work at the same rate. So to work out the problem, the first thing we can do is look at how long it takes 12 builders to build the concrete wall. Well, it takes them eight hours to build the concrete wall. But we’re told that after six hours, two of the builders have to go home.
So therefore, we can say that there’s gonna be eight minus six which is equal to two, so two hours left for 12 builders to complete the wall. So now, what we’re gonna do is work out the time for one builder to complete the wall or another way of thinking about it is the number of hours of work still needed.
And the way we’re gonna do that is by multiplying two hours by 12. And the reason we do that is cause we know that there was two hours work left for 12 builders. So therefore, we can say it would take one builder 24 hours to complete the wall or there’s 24 hours’ worth of work left.
So now, what we need to do is work out how much time it’s going to take each builder. And we know that there are 10 remaining builders. So to work this out, we’re gonna do 24 cause it’s 24 hours’ worth of work left divided by the 10 builders. So when we do that, we get 24 divided by 10 which is equal to 2.4 hours.
So is that the answer: we found out how much time is per builder? Well, no, it isn’t. And this is a really common mistake the students make because they give the answer as 2.4 hours in a question like this. But this is not what the question is actually looking for because what the question is looking for is how many extra hours does each of the remaining 10 builders have to work.
And to work out the number of extra hours, what we’re gonna do is 2.4 because that’s 2.4 hours we worked out for each builder minus the two hours that was meant to take them if they’ve been 12 builders which will give us an answer of 0.4 hours.
So we can say that each of the remaining 10 builders will have to work 0.4 hours extra to finish the wall.