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Can you please help me with this maths question?
1. An oval running track has a straight stretch of 120 m and semicircular ends of diameter 50 m. The lane are 85 m wide. How much of a headstart must runner 1 (in the innermost lane) give runner 2 (in the second lane) in order for them to cover equal distances to the finish? [ Assume both runners race along the inside edge of their lane.]
Can you please help.
How much distance is covered in one loop? That would be two straights,
plus two semicircles for the two ends, which add up to one full circle right?
The two runners cover exactly the same distance in the straight portions.
Their circle portions would be different, though, because they are running
at different diameters. The distance covered by each runner is then pi times
the diameter of the circle he's running. So runner 1 would be going pi*50,
while runner 2 would be going pi*(50+2*85). The difference between these
numbers would be pi*2*lanewidth and should be the headstart-- per loop.
In other words if the race is 10 loops long the headstart would have to be
much larger right? And you would count the loops based on the innermost
runner.
Technibond Satin-Finish Oval Link 8 Bracelet