Using direct proportion graphs

﻿Hello, my name is Mr. Clasper and today we are going to be solving proportion problems. The time taken for eight cleaners to clean an office block is six hours. If they were less clean as working, would you expect it to take more or less time to clean the office block? It would take more time for less cleaners to clean the office block. How long would it take four cleaners to clean the office block? Well, if eight cleaners took six hours and we have the number of cleaners, what do you think would happen to the time? Half as many cleaners would take twice as long. So this means four cleaners would take 12 hours to clean the office block. What assumption have we made? We've assumed that each cleaner works at the exact same rate. Given the same example, how long would it take one cleaner to clean the office block? Well, we know that it would take four cleaners is 12 hours. So we've divided the number of cleaners by two, and we've multiplied the number of hours by two. If we do the same again, this would mean that two clean is must take 24 hours and one cleaner must take 48 hours. Another way to calculate this, could it be to take the number of cleaners and multiply this by the number of hours they took, this will give us the total number of hours that it takes to clean the office block, or how many hours one cleaner would take to clean the office block. How long would it take three cleaners to clean the office block? Well, we know that one cleaner would take 48 hours or cleaning the office block takes 48 hours. So if we share this 48 hours between three cleaners, this would mean that three cleaners would take 16 hours to clean the office block. Here's some questions for you to try, pause the video, to complete your task and click resume once you're finished. And here are your solutions, so for A, to find one person, if we divide the number of people by two, we need to multiply the number of days by two, which gives us four days. This also means that to build a wall, the whole project would take four days with one person. So splitting the four days between four people for part B would mean that the whole project would take one day. And the assumption that we make in part C is that all of the people are working at the same rate. For question two, it takes four people 10 days to decorate a house. This means it would take one person 40 days. And once we have this information, we can divide 40 by three for part A and divide 40 by 10 for part B. And again, the assumption made is that all of the people are working at the same rate. Max runs 10 miles in 90 minutes, how long will it take and to run 20 miles? Well, as he has run twice as far, it will take him twice as long. Therefore it must take him 180 minutes. This is equivalent to three hours. What are Sumption have we made? We have assumed that he's going to run at the same pace for the entire 20 miles. Here are some questions for you to try, pause the video, to complete your task and click resume once you're finished. And here are your solutions, so if Matt takes four hours to cycle 36 miles, he must cycle nine miles in one hour. And now that we know that piece of information, if one hour will cover nine miles, then seven hours must cover 63 miles. And for part B, we've assumed that Matt is travelling at a constant speed. And for question four, it takes six people, eight days to repair a road. So this means there is 30 days of work for one person. If I add two more people, that means I've got eight people altogether. So a 30 divided by eight will give me 3.75, and this is 1.25 days quicker than working in five days. And again, for part B, the assumption we've made is that all the people are working at the same rate. And that brings us to the end of our lesson. We've been solving problems with proportion. Why not try the exit quiz to show off your skills? I'll hopefully see you soon.

It takes 4 workers 8 hours to dig a hole. Assuming they work at the same pace, how long would it take 1 worker to dig the same hole?

It takes 3 workers 8 hours to dig a hole. Assuming they work at the same pace, how long would it take 4 workers to dig the same hole?

Andrea drives 36 miles in 3 hours. Assuming she drives at a constant speed, how much further will she travel after a total of 5 hours?

Proportion problems

In this lesson, we will practise using ratio to solve proportion problems. We will model problems and their solutions in worded problems.

Lesson overview:Proportion problems

Core Content

Ratio 2 (Ratio and Fractions/Direct Proportion/Best Buy):