Terrible Twins
Two twins, Tom and Tyler are going to the park to play. Being competitive siblings, they devise a race around the square park which is labelled in the diagram below from A to H around the perimeter and has centre O.
Tom will run in a straight line from A to C to D to E to G to H to A, as shown in the blue diagram. Tyler will run in a perfect circle from A with centre O, passing the points C,E & G before returning to A, as shown in the green diagram.
Being twins, they run at the same constant speed. However, Tom must complete 9 laps whilst Tyler completes 10 . Who will win the race?
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1 solution
Given that they run at the same constant speed - we have to compare the distances they run.
Whoever has less to cover will win the race.
Tyler has to run 10 laps * 2*PI * R (radius of the green circle) ≈ 62.8 x R
Tom has to run 9 laps * (4 R + 2 2 2 ) ≈ (36 + 9 * 2 ) x R
Comparing the two (and getting rid of R), we see that the distance covered by Tyler ≈ 62.8 while Tom has ≈ 48,72
Therefore Tom has less to run and wins !