a        Anna, Bilal and Cai have to rake up the leaves in the garden. They each have a rake. If Anna and Bilal work together, they take 20 minutes to finish the task. If Anna and Cai work together, they take 15 minutes to finish the task. If Bilal and Cai work together, they take 12 minutes to finish the task.

How long do they take if all three of them work together?

b       A motorcycle’s wheels wear out tyres at constant, but different, rates. A tyre fitted to the front wheel would wear out after 40000 miles, but a tyre fitted to the rear wheel would wear out after 60000 miles.

i      By swapping the tyres between front and rear wheels, what is the maximum distance the owner can travel on just two tyres? When should she swap the tyres?

ii     What is the maximum distance she can travel if she also has a spare tyre? When should she swap the tyres around?

iii    If the owner fits a sidecar to his motorcycle, and a tyre fitted to the sidecar wheel would wear out after 72000 miles, what is the maximum distance she can travel on the three tyres? When should she swap the tyres around?