Question

Решите пожалуйста задачу с условием: чтобы попасть в поселок Голубые Ели автобусу с судьями нужно проехать 300 километров,а машине с техниками 120 км. Они движутся с одинаковой скоростью. Машине надо на дорогу на три часа меньше, чем автобусу. Соревнования начнутся через полчаса после того как приедут судьи. Во сколько начнутся соревнования, если автобус выехал в 6 утра и будет ехать до Голубых Елей без остановок?

Answer 1

(300-120)/3=60 км/ч
300/60=5 часов на путь автобуса
Судьи приедут в 11-00

Answer 2

Problem Analysis

To solve this problem, we need to determine the time at which the competition will start, given that a bus and a car are traveling to the village of Golubye Eli at the same speed. The bus needs to travel 300 kilometers, while the car needs to travel 120 kilometers. The car will arrive three hours earlier than the bus, and the competition will start half an hour after the judges arrive. We need to find the time at which the competition will start.

Solution

Let's break down the problem step by step:

1. Calculate the speed of the bus and the car. 2. Determine the time it takes for the car to travel 120 kilometers. 3. Calculate the time it takes for the bus to travel 300 kilometers. 4. Find the time difference between the car and the bus. 5. Calculate the time at which the judges will arrive. 6. Determine the time at which the competition will start.

Step 1: Calculate the speed of the bus and the car

Since the bus and the car are traveling at the same speed, we can assume that their speeds are equal.

Step 2: Determine the time it takes for the car to travel 120 kilometers

Let's assume that the time it takes for the car to travel 120 kilometers is t hours.

Step 3: Calculate the time it takes for the bus to travel 300 kilometers

Since the bus and the car are traveling at the same speed, the time it takes for the bus to travel 300 kilometers will be t + 3 hours.

Step 4: Find the time difference between the car and the bus

The time difference between the car and the bus is 3 hours.

Step 5: Calculate the time at which the judges will arrive

The judges will arrive half an hour before the competition starts. Let's assume the competition starts at C hours. Therefore, the judges will arrive at C - 0.5 hours.

Step 6: Determine the time at which the competition will start

To find the time at which the competition will start, we need to add the time it takes for the bus to travel 300 kilometers to the time at which the judges will arrive. Therefore, the competition will start at (C - 0.5) + (t + 3) hours.

Now, let's calculate the time at which the competition will start.

Calculation

Let's assume the competition starts at 6:00 AM (6:00). Therefore, C = 6.

From Step 2, we know that the car takes t hours to travel 120 kilometers.

From Step 3, we know that the bus takes t + 3 hours to travel 300 kilometers.

From Step 5, we know that the judges will arrive at C - 0.5 hours.

Therefore, the time at which the competition will start is (6 - 0.5) + (t + 3) hours.

To find the value of t, we can use the fact that the car travels at the same speed as the bus. Since the distance traveled by the car is 120 kilometers and the distance traveled by the bus is 300 kilometers, the ratio of their times will be the same.

Therefore, we can set up the following equation:

120 / t = 300 / (t + 3)

Solving this equation will give us the value of t.

Let's calculate the time at which the competition will start.

Calculation Continued

To find the value of t, we can solve the equation:

120 / t = 300 / (t + 3)

Cross-multiplying, we get:

120(t + 3) = 300t

Expanding and simplifying the equation, we get:

120t + 360 = 300t

Subtracting 120t from both sides, we get:

360 = 180t

Dividing both sides by 180, we get:

t = 2

Therefore, it takes the car 2 hours to travel 120 kilometers.

Now, let's calculate the time at which the competition will start.

The time at which the competition will start is:

(6 - 0.5) + (t + 3) = 5.5 + (2 + 3) = 5.5 + 5 = 10.5

Therefore, the competition will start at 10:30 AM.

Answer

The competition will start at 10:30 AM if the bus departs at 6:00 AM and travels to Golubye Eli without any stops.

Conclusion

In this problem, we calculated the time at which a competition will start based on the travel times of a bus and a car. We found that the competition will start at 10:30 AM if the bus departs at 6:00 AM and travels to Golubye Eli without any stops.