Question

Против течения паром двигается со скоростью y км/ч, а по течению в два раза быстрее. Запишите на математическом языке:A) по течению за 3 часа паром прошёл 12кмБ)по течению за 2 часа паром прошёл расстояние на 2 км большее, чем за 3 часа , двигаясь против течения

Answer 1

Скорость против течения у км/ч  
скорость по течению 2у км/ч

S=vt

а) 6у=12 у=2

б) 4у - 3у = 2
у=2

Answer 2

Problem Statement

A ferry is moving against the current at a speed of y km/h, while it moves twice as fast with the current. We need to express the following situations mathematically: A) The ferry traveled 12 km against the current in 3 hours. B) The ferry traveled a distance 2 km greater in 2 hours with the current compared to 3 hours against the current.

Mathematical Expressions

Let's define the speed of the ferry in still water as x km/h, and the speed of the current as c km/h.

1. The ferry's speed against the current is given as y km/h. - The speed of the ferry in still water minus the speed of the current equals the speed against the current: x - c = y. [[1]]

2. The ferry's speed with the current is twice as fast as against the current: y + 2c = 2(x + c). [[2]]

Solution

To solve the problem, we can use a system of equations to find the values of x and c.

1. The ferry traveled 12 km against the current in 3 hours. - We can use the formula distance = speed × time to express this situation mathematically: 12 = 3(x - c). [[3]]

2. The ferry traveled a distance 2 km greater in 2 hours with the current compared to 3 hours against the current. - Again, using the formula distance = speed × time, we can express this situation as: (x + c) × 2 = (x - c) × 3 + 2. [[4]]

Now, we can solve the system of equations to find the values of x and c.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From equation 1, we have: x - c = y. Solving for x, we get: x = y + c.

Substituting this value of x into equation 2, we have: y + 2c = 2((y + c) + c). Simplifying the equation, we get: y + 2c = 2y + 4c.

Rearranging the equation, we have: y = 2c.

Substituting this value of y into equation 1, we have: x - c = 2c. Simplifying the equation, we get: x = 3c.

Now, we have expressions for x and c in terms of c.

Solving for x and c

Substituting the expression for x into equation 3, we have: 12 = 3(3c - c). Simplifying the equation, we get: 12 = 6c.

Solving for c, we find: c = 2 km/h.

Substituting this value of c into the expression for x, we have: x = 3c = 3(2) = 6 km/h.

Therefore, the speed of the ferry in still water is 6 km/h, and the speed of the current is 2 km/h.

Conclusion

To summarize: - The speed of the ferry in still water is 6 km/h. - The speed of the current is 2 km/h.

Please let me know if there's anything else I can help you with!