A : B = 100 : 90.
A : C = 100 : 87.
B/C = (B/A*A/C) = (90/100*100/87) = 30/29
When B runs 30 m, C runs 29 m.
When B runs 180 m, C runs (29/30*180)m =174m
B beats C by (180 - 174) m = 6 m.
B covers 28 meters in 7sec. So, B's time over the course = (7/28)*100 =250 sec.
Whereas A's time over the course = 250 -7 = 243 sec.
i.e A's time over the course is 4min , 3 sec.
When B runs 25 m, A runs 45/2 m
When B runs 1000 m, A runs (45/2*1/25*1000)m = 900 m.
B beats A by 100 m.
A's speed = (5*5/15)m/sec = (25/18)m/sec
Time taken by A to cover 100 m = (100*18/15)sec = 72sec
Time taken by B to cover 92 m = (72 + 8) = 80 sec.
B's speed =(92/80*18/5)kmph =4.14kmph
Distance covered by B in 9 sec. = (100/45)*9m = 20m
A beats B by 20 metres.
To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.
While A covers 3 m, B covers 4 m.
While A covers 360 m, B covers (4/3)*360 = 480 m.
Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
A wins by 20 m.
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