A runs 4 times as fast as B. If A gives B a start of 45 m, how far must the…
2025
A runs 4 times as fast as B. If A gives B a start of 45 m, how far must the winning post be so that A and B reach it at the same time.
- A.
66 m
- B.
60 m
- C.
54 m
- D.
58 m
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Correct answer: B
Answer: 60 m
Let the finishing post be at a distance d metres from the starting point of A. B is given a start of 45 m, so B has to run (d − 45) metres while A runs d metres.
Let the speed of B be x. Then the speed of A is 4x.
Since they reach at the same time, time taken by B = time taken by A, i.e. (d − 45)/x = d/(4x).
Multiply both sides by 4x to clear denominators: 4(d − 45) = d.
Expand: 4d − 180 = d.
Rearrange: 3d = 180.
Solve: d = 180/3 = 60 m.
Therefore, the winning post must be 60 m away so that A and B reach it at the same time.