Question

Два велосипедиста отправились из одного посёлка одновременно в противоположных направлениях . Через 30 минут расстояние между ними было 15 км . Скорость одного из них 260м/мин . Узнай скорость другого велосипедиста . ( вырази 15 км в метрах) Составь и реши задачи ,обратной данной.

Answer 1

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Answer 2

Problem Statement

Два велосипедиста отправились из одного посёлка одновременно в противоположных направлениях. Через 30 минут расстояние между ними было 15 км. Скорость одного из них 260 м/мин. Узнай скорость другого велосипедиста. (вырази 15 км в метрах)

Solution

Let's solve the problem step by step:

1. Convert the given distance of 15 km to meters. Since 1 km is equal to 1000 meters, 15 km is equal to 15,000 meters.

2. Let's assume the speed of the second cyclist is x m/min.

3. The first cyclist traveled for 30 minutes at a speed of 260 m/min. Therefore, the distance traveled by the first cyclist is 260 m/min * 30 min = 7800 meters.

4. The second cyclist also traveled for 30 minutes. The total distance between the two cyclists is the sum of the distances traveled by both cyclists. Therefore, the total distance is 7800 meters + 15,000 meters = 23,800 meters.

5. The sum of the distances traveled by both cyclists is equal to the total distance between them. Therefore, we can write the equation: 7800 meters + x m/min * 30 min = 23,800 meters.

6. Now, let's solve the equation to find the value of x.

7800 + 30x = 23800

Subtract 7800 from both sides:

30x = 16000

Divide both sides by 30:

x = 16000 / 30

Simplify:

x = 533.33 m/min

Therefore, the speed of the second cyclist is approximately 533.33 m/min.

Reverse Problem

Now, let's create a reverse problem based on the given information.

Reverse Problem: Two cyclists started from the same village simultaneously in opposite directions. After 30 minutes, the distance between them was 15 km. If the speed of one cyclist is 260 m/min, find the speed of the other cyclist.

Solution:

1. The distance traveled by the first cyclist in 30 minutes is 260 m/min * 30 min = 7800 meters.

2. The total distance between the two cyclists is the sum of the distances traveled by both cyclists. Therefore, the total distance is 7800 meters + 15,000 meters = 23,800 meters.

3. Let's assume the speed of the second cyclist is x m/min.

4. The sum of the distances traveled by both cyclists is equal to the total distance between them. Therefore, we can write the equation: 7800 meters + x m/min * 30 min = 23,800 meters.

5. Now, let's solve the equation to find the value of x.

7800 + 30x = 23800

Subtract 7800 from both sides:

30x = 16000

Divide both sides by 30:

x = 16000 / 30

Simplify:

x = 533.33 m/min

Therefore, the speed of the second cyclist is approximately 533.33 m/min.