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King's Maths School

Challenge 441: Another Racing Riddle

Three aliens are racing - but how long is the race?

(Before tackling this, you might like to look back to WMC 290, which offered some inspiration!)

After settling their argument over the cake, Arglbzz, Brthflum and Clonk are having some races.

The first race is between Arglbzz and Brthflum. They each start at opposite ends of a large field and run towards each other at a constant speed. They meet 440m away from where Arglbzz started.

Next, Arglbzz races Clonk. They meet 396m away from where Arglbzz started.

Finally, Brthflum races Clonk. They meet 450m away from where Brthflum started.

How long is the field? (In other words, how far apart did the aliens start each race?)

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.