A and b 5 km race starts running in a circular field of 400 meters, if their proportion of the ratio is 5: 4, how many times the winner will cross the loser.
Answers
Answered by
0
2 times.
Suppose the speeds at which A and B run are 5x5x m/sec and 4x4x m/sec, respectively. So, in the reference frame of B, A is running at 5x−4x=x5x−4x=x m/sec speed. Since they are running in a circle of 400 m, A will again cross B after t=400/xt=400/x seconds with this relative speed (if you don't understand frame of reference, assume B is standing at a point and A is running with x m/sec speed in the circle).
So if we know overall time taken by the winner (i.e. A) to complete the race, we can divide this time by the time t, and we can find how many times A has crossed B by taking the floor of this number.
Time taken by A to run 5 km = 5000/5x seconds
Number of rounds = (5000/5x) / (400/x) = 10/4 = 2.5
Floor of this = ⌊2.5⌋=2⌊2.5⌋=2
So A will cross B two times. (We have taken floor because the integer number of times have already been crossed and fractional part is still in progress).
Suppose the speeds at which A and B run are 5x5x m/sec and 4x4x m/sec, respectively. So, in the reference frame of B, A is running at 5x−4x=x5x−4x=x m/sec speed. Since they are running in a circle of 400 m, A will again cross B after t=400/xt=400/x seconds with this relative speed (if you don't understand frame of reference, assume B is standing at a point and A is running with x m/sec speed in the circle).
So if we know overall time taken by the winner (i.e. A) to complete the race, we can divide this time by the time t, and we can find how many times A has crossed B by taking the floor of this number.
Time taken by A to run 5 km = 5000/5x seconds
Number of rounds = (5000/5x) / (400/x) = 10/4 = 2.5
Floor of this = ⌊2.5⌋=2⌊2.5⌋=2
So A will cross B two times. (We have taken floor because the integer number of times have already been crossed and fractional part is still in progress).
Similar questions