A man leaves a town at 8 a.m. on his bicycle moving at . Another man leaves the same town at 9 a.m. on his scooter moving at . At what time does he overtake the man on the bicycle?

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8: 30 a m

9 : 00 a m

9: 30 a m

10 : 00 a m

answer is C.

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Detailed Solution

Concept- We must take into account the fact that until the point of overtaking, the distance traveled by a bicycle and a scooter will be equal. Distance is calculated using the equation

, where s is the speed and

is the travel time.
Let t be the amount of time needed for the scooter to cover the distance in order to pass the bicycle.
The bicycle will require (t+1) seconds to travel the same distance. The scooter travels at 30 km/h whereas the bicycle travels at 10 km/h.
Now, employing the technique, the scooter and the bicycle will have traveled the same distance up until the time of overtaking.
i.e.

Hence, the scooter will overtake the bicycle at 9: 30 a.m.
Hence, the correct option is 3.

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