Question

Four cyclists start cycling around simultaneously with speeds of 9 m/s, 15 m/s, 25 m/s, and 33 m/s in the same direction. After how much time will they meet for the first time if the length of the track is 500 metres?

Answer 1

First and second cyclist will be meet at the track after every 500/(15 – 9) = (250/3) seconds

First and third cyclist will be meet at the track after every 500/(25 – 9) = (125/4) seconds

First and second cyclist will be meet at the track after every 500/(33 – 9) = (125/6) seconds

The time after which all the four cyclists will meet for the first time will be given by the following:

LCM [(250/3), (125.4), (125/6)]

LCM (250, 125, 125)/HCF (3, 4, 6)

250 seconds

Hence, 250 is the correct answer.