Question

Лодка шла 6 часов по течению реки со скоростью 7 км/ч и 2 часа против течения. Найди скорость лодки против течения реки, если всего она прошла 50 км.

Answer 1

1) 7*6 = 42(км) лодка прошла по течению реки
2) 50-42 = 8(км) лодка прошла против течения реки
3) 8 /2 = 4(км/ч)скорость лодки против теченияреки

Answer 2

Problem Analysis

We are given the following information: - The boat traveled downstream for 6 hours at a speed of 7 km/h. - The boat traveled upstream for 2 hours. - The total distance traveled by the boat is 50 km.

We need to find the speed of the boat when it is traveling upstream.

Solution

Let's assume the speed of the boat in still water is x km/h and the speed of the current is y km/h.

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed is (x + y) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed is (x - y) km/h.

We can set up the following equations based on the given information:

Equation 1: Distance traveled downstream = Speed downstream × Time downstream Equation 2: Distance traveled upstream = Speed upstream × Time upstream Equation 3: Total distance traveled = Distance downstream + Distance upstream

Let's solve these equations to find the values of x and y.

Calculation

Given: - Time downstream = 6 hours - Speed downstream = 7 km/h - Time upstream = 2 hours - Total distance traveled = 50 km

Using Equation 1, we can calculate the distance traveled downstream: Distance downstream = Speed downstream × Time downstream = 7 km/h × 6 hours = 42 km

Using Equation 2, we can calculate the distance traveled upstream: Distance upstream = Speed upstream × Time upstream

Using Equation 3, we can set up the equation: Total distance traveled = Distance downstream + Distance upstream 50 km = 42 km + Distance upstream Distance upstream = 50 km - 42 km = 8 km

Now, we have the values of the distance traveled downstream and upstream. We can use these values to find the speed of the boat in still water.

Using Equation 1, we can set up the equation: Distance downstream = (x + y) km/h × 6 hours 42 km = (x + y) km/h × 6 hours

Using Equation 2, we can set up the equation: Distance upstream = (x - y) km/h × 2 hours 8 km = (x - y) km/h × 2 hours

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 system of equations:

Equation 1: 42 km = (x + y) km/h × 6 hours Equation 2: 8 km = (x - y) km/h × 2 hours

Divide Equation 1 by 6: 7 km = (x + y) km/h

Divide Equation 2 by 2: 4 km = (x - y) km/h

Now, we have a system of two equations with two variables: 7 km = (x + y) km/h 4 km = (x - y) km/h

We can solve this system of equations using the method of substitution or elimination.

Let's use the method of elimination to solve the system of equations:

Multiply Equation 1 by 2: 14 km = 2(x + y) km/h

Multiply Equation 2 by 3: 12 km = 3(x - y) km/h

Now, we have the following system of equations: 14 km = 2(x + y) km/h 12 km = 3(x - y) km/h

Simplify the equations: 14 km = 2x + 2y km/h 12 km = 3x - 3y km/h

Rearrange the equations: 2x + 2y = 14 km 3x - 3y = 12 km

Multiply the first equation by 3 and the second equation by 2 to eliminate the y variable: 6x + 6y = 42 km 6x - 6y = 24 km

Add the equations: (6x + 6y) + (6x - 6y) = 42 km + 24 km 12x = 66 km

Divide both sides by 12: x = 66 km / 12 x = 5.5 km/h

Now, we have the value of x, which is the speed of the boat in still water.

To find the speed of the boat when it is traveling upstream, we can substitute the value of x into Equation 1: 7 km = (5.5 km/h + y) km/h

Simplify the equation: 7 km = 5.5 km/h + y km/h

Subtract 5.5 km/h from both sides: 7 km - 5.5 km/h = y km/h

Simplify the equation: 1.5 km = y km/h

Therefore, the speed of the boat when it is traveling upstream is 1.5 km/h.

Answer

The speed of the boat when it is traveling upstream is 1.5 km/h.