Two cyclists left two cities at the same time towards each other. One cyclist can travel the entire distance

Two cyclists left two cities at the same time towards each other. One cyclist can travel the entire distance between these cities in 6 hours, and another in 5 hours. How long after they leave will they meet? What is the distance between cities if the speed of the second cyclist is 3 km higher than the speed of the first?

1. Let’s denote the speed of the first cyclist as x km / h.

2. Let us write an expression for the speed of the second cyclist, if, according to the problem statement, it is 3 km / h more than the speed of the first.

(x + 3) km / h.

3. Let’s make an equation if it is known that the first cyclist can travel the entire path in 6 hours, and the second in 5 hours.

x * 6 = (x + 3) * 5;

6 x – 5 x = 15;

x = 15 km / h.

4. Let’s calculate the speed of the second cyclist.

x + 3 = 18 km / h.

5. Determine the distance between cities.

15 km / h * 6 h = 90 km.

6. Let’s make an equation to find out after what time t cyclists will meet.

15 * t + 18 * t = 90;

33 t = 90;

t = 2 8/11 hours.

Answer: The distance between the cities is 90 km, the cyclists will meet in 2 8/11 hours.