Two runners started at the same time in the same direction from the same place on the circular track

Two runners started at the same time in the same direction from the same place on the circular track in a multi-lap race. One hour later, when one of them had 1 km before the end of the first lap, he was informed that the second runner had completed the first lap 20 minutes ago. Find the speed of the first runner if it is known that it is 8 km / h less than the speed of the second.

Decision:

Let’s take the speed of the first runner as x, then the speed of the second runner is x + 8.

Let’s take the distance of one lap as S. Then the first runner ran S – 1 km in an hour.

Then x = (S – 1) / 1 = S – 1.

The second runner ran the entire loop in 60 – 20 = 40 minutes or 2/3 hours, which means his speed is:

x + 8 = S / (2/3);

x = S / (2/3) – 8.

Now we can make an equation and find the distance of 1 circle:

S – 1 = S / (2/3) – 8;

S – 1 = 3S / 2 – 8;

2S – 2 = 3S – 16;

-2 + 16 = 3S – 2S;

S = 14 km.

Now, knowing the distance, we can find the speed:

x = 14 – 1 = 13 km / h.

Answer: The speed of the first runner is 13 km / h.