In A Kilometre 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?

When B is given a 40metre 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 = 12 minutes 30 seconds.