Question

Теплоход,собственная скорость которого 18 км/ч , прошел 60 км по течению реки и 8 км против течения, затратив на весь путь 3 часа. Какова скорость течения реки?​

Answer 1

Ответ:

Пусть х-скорость течения реки, то

(18+х)км/ч - скорость теплохода по течению

(18-х)км/ч - скорость теплохода против течения

Составим уравнение

50              8

------- +   -------  = 3 ч

18+x         18-x

50(18-х)+8(18+х) = 3(18-х)(18+х)

900-50х+144+8х-972+3x^2=0

 3x^2 - 42x+72=0

D=1764-864=900>0

x1=12  км/ч

х2=2км/ч

По логике скорость течения реки не может быть 12 км/ч, зн. скорость будет 2 км/ч

Answer 2

Problem Analysis

We are given the following information: - The speed of the boat is 18 km/h. - The boat traveled 60 km downstream (with the current) and 8 km upstream (against the current). - The total time for the entire journey was 3 hours.

We need to find the speed of the river's current.

Solution

Let's assume the speed of the river's current is x km/h.

To solve this problem, we can use the formula: distance = speed × time.

# Downstream Journey

During the downstream journey, the boat is moving in the same direction as the current. The effective speed of the boat is the sum of its own speed and the speed of the current.

The distance traveled downstream is 60 km, and the effective speed is the boat's speed (18 km/h) plus the speed of the current (x km/h). The time taken for this part of the journey is not given.

Using the formula distance = speed × time, we can write the equation: 60 = (18 + x) × t1

# Upstream Journey

During the upstream journey, the boat is moving against the current. The effective speed of the boat is the difference between its own speed and the speed of the current.

The distance traveled upstream is 8 km, and the effective speed is the boat's speed (18 km/h) minus the speed of the current (x km/h). The time taken for this part of the journey is not given.

Using the formula distance = speed × time, we can write the equation: 8 = (18 - x) × t2

# Total Time

The total time for the entire journey is given as 3 hours. This is the sum of the time taken for the downstream journey (t1) and the time taken for the upstream journey (t2).

Using the equation t = t1 + t2, we can write: 3 = t1 + t2

# Solving the Equations

We now have a system of three equations with three unknowns: x, t1, and t2.

To solve this system, we can use substitution or elimination.

Let's solve the system using substitution.

From equation we can express t1 in terms of t2: t1 = 3 - t2 Substituting equation into equation we get: 60 = (18 + x) × (3 - t2)

Expanding and rearranging the equation, we have: 60 = 54 + 3x - 18t2 - xt2

Simplifying further, we get: 6 = 3x - 18t2 - xt2 Substituting equation into equation we get: 8 = (18 - x) × t2

Expanding and rearranging the equation, we have: 8 = 18t2 - xt2

Simplifying further, we get: 8 = 18t2 - xt2 We now have a system of two equations with two unknowns: x and t2.

Let's solve this system using elimination.

Multiplying equation by 3, we get: 24 = 54t2 - 3xt2 Subtracting equation from equation we get: 6 - 24 = 3x - 18t2 - xt2 - (54t2 - 3xt2)

Simplifying further, we get: -18 = -72t2 + 54t2

Combining like terms, we have: -18 = -18t2

Dividing both sides by -18, we get: t2 = 1

Substituting t2 = 1 into equation we get: 8 = 18 - x

Simplifying further, we have: x = 10

Therefore, the speed of the river's current is 10 km/h.

Answer

The speed of the river's current is 10 km/h.