Question

Моторная лодка проплыла по течению 105 км за 3 ч , а против течения 116 км за 4 ч . Найдите скорость течения и собственную скорость моторной лодки

Answer 1

обозначим скорость лодки за х, а скорость течения за у.составим и решим систему.
(х+у)*3=105
(х-у)*4=116
3х+3у=105
4х-4у=116
7х-у=221
у= 7х-221
3х+(3*7х-221)=105
3х+21х-663=105
24х-663=105
24х=768
32 км/чскорость моторной лодки
(32+у)*3=105
у=3км/ч скорость течения

второй способ

Узнаем скорость лодки по течению: 105/3=35 км/ч
2. Скорость лодки против течения: 116/4=29 км/ч
3. Скорость течения: (35-29)/2=3 км/ч
4.Собственная скорость лодки: (35+29)/2= 32 км/ч

ответ:3 км/ч ,32 км/ч

Answer 2

Problem Analysis

We are given that a motorboat traveled 105 km downstream in 3 hours and 116 km upstream in 4 hours. We need to find the speed of the current and the speed of the motorboat.

Downstream Speed Calculation

Let's assume the speed of the motorboat is x km/h and the speed of the current is y km/h. When the motorboat is traveling downstream, the speed of the boat relative to the ground is the sum of the boat's speed and the current's speed. Therefore, the speed of the boat downstream is (x + y) km/h.

We are given that the motorboat traveled 105 km downstream in 3 hours. Using the formula distance = speed × time, we can write the equation:

105 = (x + y) × 3.

Upstream Speed Calculation

When the motorboat is traveling upstream, the speed of the boat relative to the ground is the difference between the boat's speed and the current's speed. Therefore, the speed of the boat upstream is (x - y) km/h.

We are given that the motorboat traveled 116 km upstream in 4 hours. Using the formula distance = speed × time, we can write the equation:

116 = (x - y) × 4.

Solving the Equations

We now have a system of two equations with two variables. We can solve this system of equations to find the values of x and y.

Let's solve the equations:

From the first equation, we can express x in terms of y:

x = (105/3) - y.

Substituting this value of x into the second equation:

116 = ((105/3) - y - y) × 4.

Simplifying the equation:

116 = (35 - 2y) × 4.

Dividing both sides by 4:

29 = 35 - 2y.

Rearranging the equation:

2y = 35 - 29.

2y = 6.

Dividing both sides by 2:

y = 3.

Substituting the value of y into the first equation:

105 = (x + 3) × 3.

Simplifying the equation:

105 = 3x + 9.

Subtracting 9 from both sides:

96 = 3x.

Dividing both sides by 3:

x = 32.

Answer

The speed of the current is 3 km/h and the speed of the motorboat is 32 km/h.

Verification

Let's verify the solution using the given information:

- Downstream speed: 32 + 3 = 35 km/h. - Time taken to travel downstream: 105 km / 35 km/h = 3 hours. - Upstream speed: 32 - 3 = 29 km/h. - Time taken to travel upstream: 116 km / 29 km/h = 4 hours.

The calculated values match the given information, confirming that the solution is correct.