Question

Из пункта А в пункт В выехал велосипедист со скоростью 12км/ч. Через час навстречу ему из В в А выехал второй велосипедист со скорость 14км/ч и встретился с первым через полчаса после своего выезда. Чему равн расстояние от А до В? Успеет ли первый велосипедист преодолеть это расстояние за 2 ч?

Answer 1

12+12:2=18(км)-проехал первый
14:2=7(км) проехал второй
18+7=25(км)-от А до В
Ответ: .....
14*2=28(км)
Ответ;успеет

Answer 2

Problem Analysis

We are given the following information: - A cyclist travels from point A to point B at a speed of 12 km/h. - After an hour, another cyclist travels from point B to point A at a speed of 14 km/h. - The second cyclist meets the first cyclist half an hour after starting their journey.

We need to find: 1. The distance between points A and B. 2. Whether the first cyclist will be able to cover this distance in 2 hours.

Solution

Let's solve this problem step by step.

1. Finding the distance between points A and B: - Let's assume the distance between A and B is d km. - The first cyclist travels from A to B at a speed of 12 km/h. Therefore, the time taken by the first cyclist to cover the distance is d/12 hours. - The second cyclist travels from B to A at a speed of 14 km/h. Therefore, the time taken by the second cyclist to cover the distance is d/14 hours. - The second cyclist meets the first cyclist half an hour after starting their journey. So, the total time taken by the second cyclist is (d/14) + 0.5 hours. - The total time taken by the first cyclist is 1 hour. - Since the total time taken by both cyclists is the same, we can set up the following equation: ``` d/12 = (d/14) + 0.5 ``` - Solving this equation will give us the value of d, which is the distance between points A and B.

2. Checking if the first cyclist can cover the distance in 2 hours: - We know that the first cyclist travels at a speed of 12 km/h. - If the distance between points A and B is d km, then the time taken by the first cyclist to cover this distance is d/12 hours. - We need to check if d/12 <= 2. If this condition is true, then the first cyclist will be able to cover the distance in 2 hours.

Let's solve the equation to find the distance between points A and B.

Solution Details

1. Finding the distance between points A and B: - Let's solve the equation: d/12 = (d/14) + 0.5. - Multiplying both sides of the equation by the least common multiple (LCM) of 12 and 14, which is 84, we get: 7d = 6d + 42. - Simplifying the equation, we find: d = 42. - Therefore, the distance between points A and B is 42 km.

2. Checking if the first cyclist can cover the distance in 2 hours: - The first cyclist travels at a speed of 12 km/h. - If the distance between points A and B is 42 km, then the time taken by the first cyclist to cover this distance is 42/12 = 3.5 hours. - Since 3.5 > 2, the first cyclist will not be able to cover the distance in 2 hours.

Answer

1. The distance between points A and B is 42 km. 2. No, the first cyclist will not be able to cover this distance in 2 hours.

Please let me know if anything is unclear or if you need further assistance!