If Victoria does a job in 10 hours, and with the help of Scarlett, they can do it together in six hours, how long would it take Scarlett to do it alone?
Well, the way that we go about solving this problem is to think about how much the job Victoria, and then we’ll have a look at Scarlett, can do in one hour. Well, we’re told that Victoria takes 10 hours to do a job. So therefore, what we can say is that, in one hour, Victoria is gonna be able to do one-tenth of the job. And I’ve called the Job 𝑥. And that’s because, as we said, she does the job in 10 hours. So therefore, we divide the job, which we’re calling 𝑥, by 10. We get one-tenth of the job. So then next, what we want to work out is how much the job Victoria could do in six hours. And We can see that in six hours Victoria is able to do six-tenths of the job. And that’s because what we’ve done is multiply one hour by six to get to six hours and one-tenth by six to give us six-tenths, so six-tenths of the job.
Okay, great, but what do we do next? Well, we’re told that Scarlett helps her. And we’re told that the job is totally done in these six hours. We’ve already worked out that Victoria would’ve done six-tenths of the job in these six hours. So how much of the job is left for Scarlett to have done? Well, the amount of the job left for Scarlett to do is gonna be equal to the total job, which we’ve called 𝑥, minus the amount that Victoria could do in six hours, which is six-tenths 𝑥. And for us to work out this calculation, it might be easier to think of our 𝑥 or our job is ten-tenths of 𝑥. And that’s because a whole is the same as ten-tenths. so we’ve got ten-tenths of 𝑥 minus six-tenths of 𝑥.
So therefore, this is gonna be equal to four-tenths. And that’s because 10 minus six is four. And when we subtracting fractions with same denominator, we just subtract the numerators. So we’ve got four-tenths 𝑥, remembering that 𝑥 is what we said it would be the job. So Scarlett is gonna do four-tenths of the job in six hours. So therefore, we can set up an equation to help us find out how long it would take Scarlett to do the job.
Well, we know that Scarlett takes six hours to do four-tenths of the job. So I’m gonna set up an equation that says six is equal to four-tenths 𝑥. So therefore, if we multiply both sides by 10, we get 60 equals four 𝑥, which in context means that Scarlett could do four jobs in 60 hours. So then if Scarlett can do four jobs in 60 hours, if we want to find out how long it takes to do one job, we divide this by four. So we get 15 is equal to 𝑥. So therefore, we can conclude that it would take Scarlett 15 hours to do the job alone.