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 5000 m?

Answer 1

Oh, dude, let's break this down. So, if A gives B a 40m head start, A wins by 19 seconds. But if A gives B a 30-second head start, B wins by 40m. So, basically, they're like two kids on a playground playing tag. To find the time taken by B to run 5000m, we gotta do some math wizardry. Like, I'm talking about some serious number crunching here. So, grab your calculators and get ready for a wild ride!

Answer 2

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