Question

Расстояние между пристанями А и В =177,75км.В 9ч30мин из пристани А по течению реки отплыл катер и одновременно с ним из пристани В против течения отплыл теплоход. Собственная скорость катера 26,6км ч,а собственная скорость теплохлода 44,5 км.ч. Во сколько часов произойдёт встреча. Иследуйте,почему не дано значение скорости течения реки? ПОМОГИТЕ ПЖЛ!

Answer 1

пусть скорость реки=х, пусть они встретятся через у часов

составим уравнение - 

(26,6+х)*у+(44,5-х)*у=177,75

26,6у+ху+44,5у-ху=177,75

26,6у+44,5у=177,75

71,1у=177,75

у=2,5 часа

 

Они встретятся в 12 часов

Answer 2

Problem Analysis

To solve this problem, we need to determine the time at which the boat and the ship will meet. We are given the distance between the two ports (177.75 km), the speed of the boat (26.6 km/h), and the speed of the ship (44.5 km/h). However, the speed of the river current is not provided. We will need to find a way to solve the problem without knowing the speed of the river current.

Solution

Let's assume that the speed of the river current is x km/h. Since the boat is traveling downstream (with the current) and the ship is traveling upstream (against the current), the effective speed of the boat will be the sum of its own speed and the speed of the current, while the effective speed of the ship will be the difference between its own speed and the speed of the current.

Let's denote the time it takes for the boat and the ship to meet as t hours. During this time, the boat will travel a distance of (26.6 + x) * t km, and the ship will travel a distance of (44.5 - x) * t km. Since the total distance between the ports is 177.75 km, we can set up the following equation:

(26.6 + x) * t + (44.5 - x) * t = 177.75

Simplifying the equation, we get:

71.1t - xt = 177.75

Now, we can solve this equation to find the value of t.

Solving the Equation

To solve the equation 71.1t - xt = 177.75, we need to know the value of x (the speed of the river current). Unfortunately, the problem statement does not provide this information. However, we can still solve the equation by considering different scenarios for the speed of the river current.

Let's consider two scenarios: 1. If the speed of the river current is 0 km/h (i.e., there is no current), then the equation becomes 71.1t = 177.75. 2. If the speed of the river current is very high (approaching infinity), then the equation becomes -xt = 177.75.

In both scenarios, we can solve for t and find the time at which the boat and the ship will meet.

Scenario 1: No River Current

If we assume that there is no river current (x = 0 km/h), the equation becomes 71.1t = 177.75. Solving for t, we get:

t = 177.75 / 71.1 ≈ 2.5 hours

Therefore, if there is no river current, the boat and the ship will meet after approximately 2.5 hours.

Scenario 2: High River Current

If we assume that the speed of the river current is very high (x → ∞), the equation becomes -xt = 177.75. Solving for t, we get:

t = -177.75 / x

In this scenario, the time it takes for the boat and the ship to meet will depend on the speed of the river current. As the speed of the river current increases, the time taken for the boat and the ship to meet will decrease.

Conclusion

In conclusion, we can determine the time at which the boat and the ship will meet by solving the equation 71.1t - xt = 177.75. However, since the problem statement does not provide the speed of the river current, we can consider two scenarios: no river current and high river current. In the first scenario, where there is no river current, the boat and the ship will meet after approximately 2.5 hours. In the second scenario, where the speed of the river current is very high, the time taken for the boat and the ship to meet will depend on the speed of the river current.