In a circular race of 1600 m in length, Bhaskar and Vinay start with speeds of 27 km/h and 45 km/h starting at the same time from the same point. When will they meet for the first time on the track when running in the opposite directions and the same direction, respectively?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1 minute 20 seconds and 5 minutes 20 seconds.
Speed of Bhaskar = 27 km/h = 27 × (5/18) m/s = 7.5 m/s
Speed of Vinay = 45 km/h = 45 × (5/18) m/s = 12.5 m/s
Relative speed when they are running in the opposite direction = 7.5 + 12.5 = 20 m/s
Time required to meet = 1600/20 = 80 seconds = 1 minute 20 seconds
Relative speed when they are running in the same direction = 12.5 - 7.5 = 20 m/s
When running in the same direction, their relative speed is the difference of their speeds: 12.5 m/s - 7.5 m/s = 5 m/s
Time required to meet = 1600/5 = 320 seconds = 5 minutes 20 seconds
Therefore, they meet for the first time on the track after 1 minute 20 seconds and 5 minutes 20 seconds when running in opposite directions and the same direction, respectively.