Question

Лучшие друзья Болек и Лёлек одновременно стартовали из пункта AA в пункт BB и всё время двигались вдоль прямой. Скорость Болека равна V1=6 км/чV1=6 км/ч, а Лёлека – V2=5 км/чV2=5 км/ч. В тот же момент между ними начала бегать собака со скоростью U=11 км/чU=11 км/ч, причём её скорость одинакова при движении в обоих направлениях. Через некоторое время Болек дошёл до конечного пункта и решил подождать своего друга. Собака при этом продолжила свои пробежки между мальчиками до тех пор, пока они не встретились. Определите суммарный путь, который преодолела собака, если Болек пришёл в пункт B на τ=3 минτ=3 мин раньше своего друга. Ответ выразите в кмкм, округлив до десятых. Временем, которое собака тратит на разворот, можно пренебречь. помогите ставлю 25 баллов

Answer 1

Собака бегала столько же времени, сколько шёл Лёлек
3мин=1/20ч
х- время Болека
х+1/20 время Лёлека
6х=5(х+1/20)
6х=5х+0,25
х=0,25ч
0,25+1/20=1/4+1/20=5/20+1/20=6/20=0,3ч время Лёлека и собаки
11*0,3=3,3 км
ответ: 3,3 км

Answer 2

To solve this problem, we need to determine the total distance covered by the dog while it was running between the boys. Let's break down the problem step by step.

Given Information:

- Bolik's speed (V1) = 6 km/h - Lolek's speed (V2) = 5 km/h - Dog's speed (U) = 11 km/h - Bolik arrived at point B τ = 3 min (or 0.05 hours) before Lolek

Approach:

1. Calculate the time it took Bolik to reach point B. 2. Calculate the time it took Lolek to reach point B. 3. Calculate the distance covered by the dog during this time.

Step 1: Calculate Bolik's time to reach point B:

The time it took Bolik to reach point B can be calculated using the formula: Time = Distance / Speed

Let's assume the distance between point A and point B is 'd' km.

The time taken by Bolik to reach point B is: Time taken by Bolik = d / V1

Step 2: Calculate Lolek's time to reach point B:

Since Lolek arrived τ = 3 min (or 0.05 hours) after Bolik, we can calculate the time taken by Lolek to reach point B as: Time taken by Lolek = Time taken by Bolik + τ

Step 3: Calculate the distance covered by the dog:

The dog runs between Bolik and Lolek until they meet. During this time, the dog's speed is U = 11 km/h.

Let's assume the time taken by the dog to meet Bolik is 't' hours.

The distance covered by the dog while running between Bolik and Lolek is: Distance covered by the dog = U * t

Final Step: Calculate the total distance covered by the dog:

To find the total distance covered by the dog, we need to determine the time taken by Lolek to reach point B and then calculate the distance covered by the dog during that time.

Let's substitute the values and solve the problem.

Solution:

1. Calculate Bolik's time to reach point B: - Time taken by Bolik = d / V1

2. Calculate Lolek's time to reach point B: - Time taken by Lolek = Time taken by Bolik + τ

3. Calculate the distance covered by the dog: - Distance covered by the dog = U * (Time taken by Lolek - Time taken by Bolik)

4. Calculate the total distance covered by the dog: - Total distance covered by the dog = Distance covered by the dog

Let's calculate the values step by step.

Step 1: Calculate Bolik's time to reach point B:

The time taken by Bolik to reach point B is: Time taken by Bolik = d / V1 [[1]]

Step 2: Calculate Lolek's time to reach point B:

The time taken by Lolek to reach point B is: Time taken by Lolek = Time taken by Bolik + τ [[1]]

Step 3: Calculate the distance covered by the dog:

The distance covered by the dog is: Distance covered by the dog = U * (Time taken by Lolek - Time taken by Bolik) [[1]]

Step 4: Calculate the total distance covered by the dog:

The total distance covered by the dog is: Total distance covered by the dog = Distance covered by the dog [[1]]

Let's substitute the values and calculate the solution.

Solution:

1. Calculate Bolik's time to reach point B: - Time taken by Bolik = d / V1 = d / 6 km/h

2. Calculate Lolek's time to reach point B: - Time taken by Lolek = Time taken by Bolik + τ = (d / 6 km/h) + 0.05 hours

3. Calculate the distance covered by the dog: - Distance covered by the dog = U * (Time taken by Lolek - Time taken by Bolik) = 11 km/h * [(d / 6 km/h) + 0.05 hours - (d / 6 km/h)]

4. Calculate the total distance covered by the dog: - Total distance covered by the dog = Distance covered by the dog

To find the exact value of the total distance covered by the dog, we need the value of 'd' (the distance between point A and point B). Unfortunately, the problem statement does not provide this information. Please provide the value of 'd' so that we can calculate the total distance covered by the dog accurately.

Please let me know if you need any further assistance.