Two persons are to run a race, but one can run 8 meters per second, whereas the other can run 2 meters per second. If the slower runner has a 99-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?

They ran for the same length of time

let the time be t seconds

then distance covered by faster runner = 8t
distance covered by slower runner = 2t

so 8t - 2t = 99
6t = 99
t = 99/6 or 16.5 seconds

Two persons are to run a race, but one can run 8 meters per second, whereas the other can run 2 meters per second. If the slower runner has a 81-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?

To find out how long it will take for the faster runner to catch up with the slower runner, we can set up an equation based on their relative speeds and the head start.

Let's assume that it takes t seconds for the faster runner to catch up with the slower runner.

In that time, the slower runner would have covered a distance of 2t meters (since they can run at a rate of 2 meters per second).

The faster runner, on the other hand, would have covered a distance of 8t meters (since they can run at a rate of 8 meters per second).

Since the slower runner had a 99-meter head start, we can set up the equation:

2t + 99 = 8t

Subtracting 2t from both sides:

99 = 6t

Now, divide both sides by 6:

t = 99 / 6

Simplifying:

t ā‰ˆ 16.5

Therefore, it will take approximately 16.5 seconds for the faster runner to catch up with the slower runner.

To find out how long it will take for the faster runner to catch up with the slower runner, we need to determine the rate at which the faster runner is closing the gap between them.

The slower runner has a head start of 99 meters, which means that when the faster runner starts running, the slower runner is already 99 meters ahead.

Now, let's calculate the rate at which the faster runner is gaining on the slower runner. The faster runner runs at a speed of 8 meters per second, while the slower runner runs at a speed of 2 meters per second. This means that the faster runner gains 8 - 2 = 6 meters per second on the slower runner.

To catch up to the slower runner, the faster runner needs to close the 99-meter gap between them. Therefore, the time it will take for the faster runner to catch up to the slower runner can be calculated by dividing the total distance (99 meters) by the rate at which the faster runner is gaining on the slower runner (6 meters per second):

Time = Distance / Rate
Time = 99 meters / 6 meters per second

Calculating this gives us:
Time ā‰ˆ 16.5 seconds

So, it will take approximately 16.5 seconds for the faster runner to catch up with the slower runner if they start at the same time.