Video: Pack 4 • Paper 2 • Question 15

Pack 4 • Paper 2 • Question 15

02:57

Video Transcript

On Monday, it took four bricklayers three and a half hours to build a two-meter-by-three-meter wall. On Tuesday, only three of the four bricklayers were available. Assume that all the bricklayers worked at the same rate over the two days. Each bricklayer is paid 11 pounds for each hour, or part of an hour that they work. How much did each bricklayer earn for the time they spent building an identical wall on Tuesday?

The first sentence tells us that it took four people three and a half hours to build the wall. Our first step is to work out how long it would take one person to build the same wall.

To get from four people to one person, we can divide by four. So our first thought might be to divide three and a half hours by four. However, this would give us a shorter time. And clearly it would take one person longer to build the wall than it would take four people.

This means that we need to multiply the time by four. It would take one person four times as long to build the wall as it would take four people. Three and a half hours multiplied by four is 14 hours, as 3.5 multiplied by four is equal to 14.

On the Tuesday, only three of the four bricklayers were available. We now need to work out how long it would take three people to build an identical wall. In order to calculate this, we need to divide 14 by three, as three people would build a wall three times as fast as one person. 14 divided by three, or fourteen thirds, is the same as four and two-thirds. Therefore, it would take three people four and two-thirds hours to build an identical wall.

At this stage, it is worth checking that the amount of time it would take three bricklayers is greater than the amount of time it would take four bricklayers. In this case, four and two-thirds hours is greater than three and a half hours.

As the bricklayers get paid 11 pounds for each hour, or part of an hour, we need to round four and two-thirds up to the nearest whole number. In this case, we need to round it up to five hours. The bricklayers will be paid for five hours of work. 11 pounds multiplied by five is equal to 55 pounds. This means that each bricklayer will earn 55 pounds for building the wall on Tuesday.

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