The cyclist traveled the AB path at a speed of 12 km / h. Returning from B to A, he developed a speed of 18 km / h

The cyclist traveled the AB path at a speed of 12 km / h. Returning from B to A, he developed a speed of 18 km / h and spent 15 minutes less on the way back than on the way …

Let’s convert minutes to hours:
15 minutes = 0.25 hours.

Let the distance between cities A and B be x kilometers.
The cyclist spent x / 12 hours on the way from A to B. On the way back it took x / 18 hours. Let’s make an equation, knowing that the cyclist came back 0.25 hours faster:
x / 12 – x / 18 = 0.25;
6 * x = 54;
x = 9 km is the distance between A and B.

Let’s check.
Let’s find how long it took a cyclist to travel from A to B:
9/12 = 0.75 h.
Let’s determine how long it took on the way back:
9/18 = 0.5 h.
0.75 – 0.5 = 0.25 h.

Answer: The distance between cities A and B is 9 kilometers.