Time, Speed and Distance Question 10 - CAT 2020
Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?
Step-by-Step Explanation
The time taken for multiple runners to meet back at the starting point depends on their individual lap completion times:
Lap Time₍Anil₎ = 3 km/15 km/hr = 1/5 hour
Lap Time₍Sunil₎ = 3 km/10 km/hr = 3/10 hour
Find the first time Anil and Sunil meet at the starting point together by taking the LCM of their lap times:
Meeting Time = LCM(1/5, 3/10) = LCM(1, 3)/HCF(5, 10) = 3/5 hour
Calculate the total distance Ravi covers at his constant speed of 8 km/hr during this time frame:
Distance covered by Ravi = 8 km/hr × 3/5 hour = 24/5 = 4.8 km
Correct Option: A
💡 FundaMakers Tip:
When finding when runners meet at the starting point, you don't need to track their relative speed or position along the track. Simply find the LCM of their individual lap times. This gives you the exact time window, which you can multiply directly by Ravi's speed to find his distance in one step.