In a kilo meter race, if A gives B a 40 m start, A wins by 19 s. But if A gives B a 30 s start, B wins by 40 m. Find the time taken by B to run 5,000 m?  Choose one
A) 150 s
B) 450 s
C) 750 s
D) 825 s
E) 925 s

Rationale: when b is given a 40 m start then b runs 960 m in t secs and a runs 1000 m in t - 19 secs . when b is given a 30 second start then b runs 1000 m in t secs and a runs 960 m in t - 30 secs . assume that the speed of a ( va ) and b ( vb ) is constant in both situations . then vb = 960 ÷ t = 1000 ÷ t , and va = 1000 ÷ ( t - 19 ) = 960 ÷ ( t - 30 ) so 960 t = 1000 t , and 1000 t - 30000 = 960 t - 18240 . then 40 t = - 40 t + 11760 , t = - t + 294 . substituting for t in 960 t = 1000 t gives : - 960 t + 282240 = 1000 t 1960 t = 282240 t = 144 b ' s speed is 960 / t = 960 / 144 = 6.67 metres per second . assuming the same constant speed to run 5000 metres then the time taken is 5000 / 6.67 = 750 seconds answer : c
Answer: C