Two runners start at the same point and jog at a constant speed along a straight path. Runner A starts at time t = 0 s, and Runner B starts at time t = 2.5 s. The runners both reach a distance 64 m from the starting point at time t = 25 s. If the runners continue at the same speeds, how far from the starting point will each be at time t = 45 s?

See explanation below

Explanation:

First thing to do here, is to calculate the speed of each runner. The problem states that both runners jog at a constant speed. We are given data for both runners, the starting time and the time where both of them reach the same distance.

With these data we can calculate the speed of both runners. Let's do it with runner 1:

If by t  = 25 s it reach a 64 m of distance, then his speed:

V = d/t   (1)

Replacing we have:

V₁ = 64 / 25 = 2.56 m/s

With this speed we can calculate the distance at t = 45 s so:

d = V * t    (2)

d₁ = 2.56 * 45

d₁ = 115.2 m

So Runner 1 will be at 115.2 from the starting point at 45 seconds.

For runner 2, he began at t = 2.5 s, but he reach the 64 m at 25 s, so his speed would be:

V₂ = 64 / (25-2.5) = 2.84 m/s

And the distance at t = 45 s

d₂ = 2.84 * 45

d₂ = 127.8 m

Runner 2 is 127.8 m from the starting point at 45 seconds.

Hope this helps

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