Question

из одного пункта одновременно в противоположных направлениях выехали два велосипеда. скрость одного из них составляет 5/6 скорости второго. Найдите скорость каждого велосипедиста, если через 40 минут расстояние между ними составило 22 км.

Answer 1

х км/ч скорость 1 велосипедиста

5х/6 км/ч скорость 2 велосипедиста

40 мин = 40/60 = 2/3

2х/3 км проехал 1 велосипедист

5х/6 * 2/3 = 5х/9 км проехал 2 велосипедист

2х/3 + 5х/9 = 22

6х + 5х = 22 * 9

11х = 198

х = 18

18 км/ч скорость 1 велосипедиста

5 * 18/6 = 15 км/ч скорость 2 велосипедиста

Answer 2

Problem Analysis

We are given that two bicycles start from the same point in opposite directions. The speed of one bicycle is 5/6 times the speed of the other bicycle. After 40 minutes, the distance between them is 22 km. We need to find the speed of each cyclist.

Solution

Let's assume the speed of the first cyclist is x km/h. Then the speed of the second cyclist will be (5/6)x km/h.

We know that distance = speed × time. Since both cyclists have been traveling for 40 minutes (or 40/60 = 2/3 hours), we can set up the following equation:

Distance covered by the first cyclist + Distance covered by the second cyclist = Total distance

(x × 2/3) + ((5/6)x × 2/3) = 22

Simplifying the equation:

(2/3)x + (10/18)x = 22

(12/18)x + (10/18)x = 22

(22/18)x = 22

x = (22 × 18) / 22

x = 18

So, the speed of the first cyclist is 18 km/h, and the speed of the second cyclist is (5/6) × 18 = 15 km/h.

Answer

The speed of the first cyclist is 18 km/h, and the speed of the second cyclist is 15 km/h.

Explanation

The first cyclist is traveling at a speed of 18 km/h, while the second cyclist is traveling at a speed of 15 km/h. After 40 minutes (2/3 hours), the first cyclist will have covered a distance of (18 × 2/3) = 12 km, and the second cyclist will have covered a distance of (15 × 2/3) = 10 km. The sum of these distances is 12 km + 10 km = 22 km, which matches the given total distance. Therefore, the solution is correct.