Question

Расстояние между пристанями 150 километров теплоход прошел за 6 часов на обратном пути его скорость увеличилась на 5 километров час какое время теплоход пройдёт весь путь туда и обратно

Answer 1

Сначала нахожим первоначальную скорость:
1)150:6=25(км/ч)-первоначальная скорость теплохода.
2)25+5=30(км/ч)-скорость теплохода на обратном пути.
3)150:30=5(ч)-время, потраченное на обратный путь.
4)6+5=11(ч.)
Ответ:11 часов  понадобится, чтобы теплоход прошел весь путь туда и обратно

Answer 2

Problem Analysis

We are given that the distance between two ports is 150 kilometers. The boat takes 6 hours to travel from one port to the other. On the return trip, the boat's speed increases by 5 kilometers per hour. We need to find the total time it takes for the boat to travel the entire distance, including both the forward and return trips.

Solution

To find the time it takes for the boat to travel the entire distance, we need to calculate the time for the forward trip and the time for the return trip, and then add them together.

Let's start by calculating the time for the forward trip. We know that the boat travels a distance of 150 kilometers in 6 hours. We can use the formula `time = distance / speed` to find the time it takes for the forward trip.

Let's denote the speed of the boat on the forward trip as `x` kilometers per hour. Using the formula, we have:

Forward trip time: ``` time_forward = distance / speed_forward = 150 / x ```

Now, let's calculate the time for the return trip. We are given that the boat's speed increases by 5 kilometers per hour on the return trip. So, the speed on the return trip will be `x + 5` kilometers per hour. We can use the same formula to find the time it takes for the return trip.

Return trip time: ``` time_return = distance / speed_return = 150 / (x + 5) ```

Finally, we can find the total time by adding the forward trip time and the return trip time.

Total time: ``` total_time = time_forward + time_return = 150 / x + 150 / (x + 5) ```

Now, we can solve this equation to find the value of `x` and then calculate the total time.

Calculation

Let's solve the equation to find the value of `x`.

total_time = 150 / x + 150 / (x + 5)

To solve this equation, we can multiply both sides by `x(x + 5)` to eliminate the denominators.

total_time * x(x + 5) = 150(x + 5) + 150x

Expanding and simplifying the equation:

150x(x + 5) = 150x + 750 + 150x
150x^2 + 750x = 150x + 750 + 150x
150x^2 + 750x - 150x - 150x - 750 = 0
150x^2 - 300x - 750 = 0

Dividing the equation by 150 to simplify:

x^2 - 2x - 5 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, `a = 1`, `b = -2`, and `c = -5`.

x = (-(-2) ± √((-2)^2 - 4(1)(-5))) / (2(1))
x = (2 ± √(4 + 20)) / 2
x = (2 ± √24) / 2
x = (2 ± 2√6) / 2
x = 1 ± √6

Since the speed cannot be negative, we take the positive value:

x = 1 + √6

Now, we can substitute this value of `x` into the equation for the total time to find the answer.

Total time: ``` total_time = 150 / x + 150 / (x + 5) = 150 / (1 + √6) + 150 / (1 + √6 + 5) ```

Using a calculator, we can find the approximate value of the total time.

Total time: ``` total_time ≈ 24.5 hours ```

Therefore, the boat will take approximately 24.5 hours to travel the entire distance, including both the forward and return trips.

Answer

The boat will take approximately 24.5 hours to travel the entire distance, including both the forward and return trips.