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oger and Caine are in a foot race. Roger is 200m ahead of Caine. However, Caine is unning10m/s while Roger is only unning at 8m/s. After what length of time would Caine take to be100m ahead of Roger?

Question

oger and Caine are in a foot race. Roger is 200m ahead of Caine. However, Caine is �unning10m/s while Roger is only �unning at 8m/s. After what length of time would Caine take to be100m ahead of Roger?

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Solution

First, let's determine when Caine will catch up to Roger.

Roger is 200m ahead of Caine. Caine runs at a speed of 10m/s and Roger runs at a speed of 8m/s. Therefore, Caine is closing the gap at a rate of 2m/s (10m/s - 8m/s).

To find out when Caine will catch up to Roger, we divide the initial distance between them by the rate at which Caine is closing the gap:

200m / 2m/s = 100 seconds

So, Caine will catch up to Roger after 100 seconds.

Next, we need to find out when Caine will be 100m ahead of Roger. Since Caine continues to run 2m/s faster than Roger, we divide the additional distance Caine needs to run by his speed advantage:

100m / 2m/s = 50 seconds

Therefore, Caine will be 100m ahead of Roger 50 seconds after catching up to him.

Finally, we add the time it takes for Caine to catch up to Roger to the time it takes for him to get 100m ahead:

100 seconds + 50 seconds = 150 seconds

So, Caine will be 100m ahead of Roger after 150 seconds.

This problem has been solved

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