Question

Моторная лодка проплыла 48 км по течению реки за 3 часа, а против течения то же расстояние за 4 часа. найдите скорость течения реки и сообственную скорость моторной лодки

Answer 1

48:3=16 км/ч ск. по течению
48:4=12 км/ч ск. против теч.
16-12=4 км/ч удвоенная ск. реки
4:2=2 км/ч собств. ск. реки
16-2=14 км/ч или 12+2=14 км/ч ск. лодки

Answer 2

Problem Analysis

We are given that a motorboat traveled a distance of 48 km downstream in 3 hours and the same distance upstream in 4 hours. We need to find the speed of the river's current and the speed of the motorboat.

Downstream Speed Calculation

To find the speed of the river's current, we can use the formula:

Downstream Speed = Boat Speed + Current Speed

Let's assume the speed of the motorboat is represented by B and the speed of the river's current is represented by C.

Given that the motorboat traveled 48 km downstream in 3 hours, we can set up the equation:

48 km = (B + C) km/h * 3 hours

Simplifying the equation, we have:

48 km = 3B + 3C

Upstream Speed Calculation

Similarly, to find the speed of the river's current, we can use the formula:

Upstream Speed = Boat Speed - Current Speed

Using the same assumptions as before, we can set up the equation:

48 km = (B - C) km/h * 4 hours

Simplifying the equation, we have:

48 km = 4B - 4C

Solving the Equations

We now have a system of two equations with two unknowns:

Equation 1: 48 km = 3B + 3C

Equation 2: 48 km = 4B - 4C

We can solve this system of equations to find the values of B and C.

Solution

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, we can express C in terms of B:

C = (48 km - 3B) / 3

Substituting this value of C into Equation 2, we have:

48 km = 4B - 4((48 km - 3B) / 3)

Simplifying the equation, we get:

48 km = 4B - (64 km - 4B)

Simplifying further, we have:

48 km = 4B - 64 km + 4B

Combining like terms, we get:

112 km = 8B

Dividing both sides by 8, we find:

B = 14 km/h

Substituting this value of B back into Equation 1, we can find C:

48 km = 3(14 km/h) + 3C

Simplifying the equation, we have:

48 km = 42 km/h + 3C

Subtracting 42 km/h from both sides, we get:

6 km = 3C

Dividing both sides by 3, we find:

C = 2 km/h

Answer

The speed of the river's current is 2 km/h and the speed of the motorboat is 14 km/h.

Verification

Let's verify our solution by substituting the values of B and C back into the original equations:

Equation 1: 48 km = 3B + 3C

Substituting B = 14 km/h and C = 2 km/h, we have:

48 km = 3(14 km/h) + 3(2 km/h)

Simplifying the equation, we get:

48 km = 42 km/h + 6 km/h

Combining like terms, we have:

48 km = 48 km

The equation is true, which verifies our solution.

Equation 2: 48 km = 4B - 4C

Substituting B = 14 km/h and C = 2 km/h, we have:

48 km = 4(14 km/h) - 4(2 km/h)

Simplifying the equation, we get:

48 km = 56 km/h - 8 km/h

Combining like terms, we have:

48 km = 48 km

The equation is true, which verifies our solution.

Therefore, our solution is correct. The speed of the river's current is 2 km/h and the speed of the motorboat is 14 km/h.