Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 6 meters per second. If the slower runner has a 70-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?

the speed difference is 4m/s

The distance difference is 70m.

so, the faster runner will take 70/4=17.5s to catch up

To solve this problem, we can use the formula for calculating time:

Time = Distance / Speed

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

At time 't', the distance covered by the faster runner (10m/s) would be equal to the distance covered by the slower runner (6m/s) plus the head start distance (70m).

Using the formula mentioned earlier, we can set up the equation:

10t = 6t + 70

Now, we can solve the equation for 't':

10t - 6t = 70
4t = 70
t = 70/4
t = 17.5 seconds

Therefore, it will take 17.5 seconds for the faster runner to catch up to the slower runner if they both begin at the same time.