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 the correct answer:
A) 150 s  B) 450 s  C) 750 s  D) 825 s  E) 925 s
When B is given a 40 m start then B runs 960m in T secs and A runs 1000m in T-19 secs.   When B is given a 30 second start then B runs 1000m in t secs and A runs 960m 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 960t = 1000T, and 1000t - 30000 = 960T - 18240. Then 40t = -40T + 11760, t = -T + 294.   Substituting for t in 960t = 1000T   gives : -960T + 282240 = 1000T   1960T = 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:750 s
<result>C</result>
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?