# A cyclist left point A to point B at a speed of 23 km / h, and at the same time a second cyclist left point B to A

March 29, 2021 | education

| **A cyclist left point A to point B at a speed of 23 km / h, and at the same time a second cyclist left point B to A at a speed of 19 km / h. When the first cyclist arrived at point B, the second still had 24 km / h to go to point A. What is the distance between A and B.**

Let’s denote the distance between points A and B by the letter x.

Let us express the time from A to B of the first cyclist: x / 23.

The second cyclist covered (x – 24) km during this time. Let’s express its travel time: (x – 24) / 19.

We make the equation: x / 23 = (x – 24) / 19.

According to the rule of proportion: 23 (x – 24) = 19x;

23x – 552 = 19x;

23x – 19x = 552;

4x = 552;

x = 552/4 = 138 (km).

Answer: the distance between A and B is 138 km.

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