Problem Solving Unit

Year 9 Interactive Maths - Second Edition

Problem 10.1 Mixture
A cylinder contains 100 litres of water. A certain quantity of water is drained and replaced by vinegar. After the contents of the cylinder are thoroughly stirred, the same amount of the mixture is again drained and replaced by vinegar. The final mixture contains water and vinegar in the ratio 1:3, respectively. How many litres are drained each time?
Problem 10.2 Track
P and Q run around a circular track at uniform speeds in opposite directions, starting from diametrically opposite points. If they start at the same time, meet first after Q has travelled 80 metres; and meet a second time 40 metres before P has completed one lap, find the circumference of the track.
Problem 10.3 Mown Strip
Two brothers are given the job of mowing a rectangular lawn that measures 100 metres by 80 metres. They have decided to share the work by mowing one half of the area each. The brother who begins the job starts by cutting a strip all the way around the edge of the lawn and continuing around in this manner until his share of the job is completed. How wide will this mown strip be when he finishes his share?
Problem 10.4 Triangles and Squares
What is the area of the square EFGH?

Please read the Terms and Conditions of Use of this Website and our Privacy and Other Policies.
If you experience difficulties when using this Website, tell us through the feedback form or by phoning the contact telephone number.