In a 120 metre race. P beats S by 6 meters. If S starts with a head start of 7.5 metres and it is a 100 metre race, then who wins the race and how many metres? (Correct to 2 decimal places)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. S, 2.63.
Speed of S/Speed of P = 114/120 = 0.95
Total race length = 100 m
S gets a head start of 7.5 metres, so S only needs to run 92.5 metres
Let P's speed = x then S's speed = 0.95x
Time taken by P to run 100 metres = 100/x
In that time, S runs = 0.95x(100/x) = 95 m
Time S takes to run 92.5 metres = 92.5/(0.95x)
In that time, P runs = x(92.5/0.95x) = 92.5/0.95 = 97.37 m (approx)
100 - 97.37 = 2.63 m
Therefore, S wins by 2.63 metres.