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King's Maths School

Challenge 459: Pipe Dream

How fast can these pipes fill a container?

Here are some variants on a classic problem style - can you dream up any of your own?

(1) Two pipes are filling a tank at a constant rate. On its own, pipe A could fill the tank in 4 minutes, while pipe B could fill the tank in 6 minutes. However, there is a leak in the bottom of the tank, which lets out liquid at a constant rate; a full tank would empty in 12 hours. 

If both pipes are turned on, how long will it take to fill an empty tank?

(2) Three pipes are filling a tank at a constant rate. Together, pipes A and B could fill the tank in 3 minutes; pipes B and C could fill the tank in 4 minutes; pipes A and C could fill the tank in 6 minutes.

If all three pipes are turned on, how long will it take to fill an empty tank?

(3) Five pipes are filling a tank at a constant rate. Together, they take 3 minutes to fill an empty tank. On its own, the slowest of the pipes would take 36 minutes to fill an empty tank.

What is the fastest that any of the pipes could fill the tank on its own?

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.