Question

5. Два велосипедиста, находясь друг от друга на расстоянии 9 км, выехали одновременно навстречу друг другу и через 20 мин встретились. Когда же они выехали из одного пункта в одном направлении, то через 1ч 40 мин один отстал от другого на 5 км. Какова скорость каждого велосипедиста?

Answer 1

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Answer 2

Calculating the Speed of Each Cyclist

To calculate the speed of each cyclist, we can use the formula: speed = distance / time.

1. Meeting Each Other: - The cyclists meet after 20 minutes. - The combined distance they cover is 9 km. - Let's calculate the combined speed using the formula: speed = distance / time.

The combined speed when they meet is: - speed = 9 km / (20 min / 60) = 27 km/h.

2. Moving in the Same Direction: - One cyclist falls 5 km behind the other after 1 hour and 40 minutes. - Let's calculate the speed of each cyclist using the relative speed concept.

The relative speed when one cyclist falls 5 km behind the other is: - relative speed = 5 km / (1 hour + 40 min) = 3 km/h.

Let's denote the speed of the faster cyclist as x km/h and the speed of the slower cyclist as y km/h.

- The relative speed of the two cyclists moving in the same direction is the difference of their speeds: x - y. - We also know that the combined speed when they meet is 27 km/h.

Using these two pieces of information, we can set up the following equations: - x + y = 27 (when moving towards each other) - x - y = 3 (when moving in the same direction)

Solving these equations will give us the speeds of the two cyclists.

Solving for the Speed of Each Cyclist

Let's solve the system of equations to find the speeds of the two cyclists.

Adding the two equations together, we get: - 2x = 30 - x = 15 km/h

Substituting the value of x in the equation x + y = 27, we get: - 15 + y = 27 - y = 12 km/h

So, the speed of the first cyclist is 15 km/h and the speed of the second cyclist is 12 km/h.

Therefore, the speed of the first cyclist is 15 km/h and the speed of the second cyclist is 12 km/h.