Question

Из села одновременно в противоположных направлениях выехали два велосипедиста. скорость одного из них составляет 5/6 скорости другого. найдите скорость каждого велосипедиста, если через 2/3 часа расстояние между ними составило 22 км?

Answer 1

Скорость 1-го, пусть будет 5/6х, а скорость 2-го - х, тогда 40 минут = 2/3 часа, составим уравнение: (5\6х+х)*2/3= 22
11/6х=22*3/2=33
х=33*6/11=18
скорость 1-го 18*5/6= 15, а скорость 2-го 18 км/ч

Answer 2

Problem Analysis

We are given that two cyclists start simultaneously from a village in opposite directions. The speed of one cyclist is 5/6 times the speed of the other cyclist. After 2/3 hours, the distance between them is 22 km. We need to find the speed of each cyclist.

Solution

Let's assume the speed of one cyclist is x km/h. Then the speed of the other cyclist would be (5/6)x km/h.

We can use the formula distance = speed × time to calculate the distance covered by each cyclist in 2/3 hours.

For the first cyclist: Distance covered = Speed × Time = x × (2/3) km

For the second cyclist: Distance covered = Speed × Time = (5/6)x × (2/3) km

According to the problem, the sum of the distances covered by both cyclists is 22 km. So we can write the equation:

(x × (2/3)) + ((5/6)x × (2/3)) = 22

Simplifying the equation: (2/3)x + (10/18)x = 22

Combining like terms: (12/18)x = 22

Simplifying further: (2/3)x = 22

To solve for x, we can multiply both sides of the equation by (3/2): x = (22 × (3/2))

Simplifying: x = 33

Therefore, the speed of the first cyclist is 33 km/h and the speed of the second cyclist is (5/6) × 33 = 27.5 km/h.

Answer

The speed of the first cyclist is 33 km/h and the speed of the second cyclist is 27.5 km/h.