Question

Лодка 30 км проходит за 3 часа по течению реки и 28 км за 4 часа против течения. Найдите скорость течения реки и собственную скорость лодки

Answer 1

Ну тут получается 30/3=10км/ч
потом делишь 28/4=7км/ч
10-7=3-разница в скорости
пото 3/2=1.5-течение реки
и 8.5-скорость лодки

Answer 2

Problem Analysis

We are given that a boat travels 30 km downstream in 3 hours and 28 km upstream in 4 hours. We need to find the speed of the river's current and the speed of the boat.

Downstream Speed Calculation

To find the speed of the boat downstream, we can use the formula: distance = speed × time. Let's denote the speed of the boat as B and the speed of the river's current as C. The boat's speed downstream will be the sum of its own speed and the speed of the current, so we have:

30 km = (B + C) × 3 hours.

Upstream Speed Calculation

Similarly, to find the speed of the boat upstream, we can use the same formula: distance = speed × time. The boat's speed upstream will be the difference between its own speed and the speed of the current, so we have:

28 km = (B - C) × 4 hours.

Solving the Equations

We now have a system of two equations with two unknowns (B and C). We can solve this system of equations to find the values of B and C.

Let's solve the equations step by step:

From the first equation, we have: 30 = (B + C) × 3.

From the second equation, we have: 28 = (B - C) × 4.

We can simplify the equations further:

Equation 1: 30 = 3B + 3C. Equation 2: 28 = 4B - 4C.

Now, we can solve this system of equations using any method, such as substitution or elimination.

Solution

To solve the system of equations, we can use the elimination method. We'll multiply Equation 1 by 4 and Equation 2 by 3 to eliminate the variable C:

Equation 1 (multiplied by 4): 120 = 12B + 12C. Equation 2 (multiplied by 3): 84 = 12B - 12C.

Adding the two equations together, we get: 120 + 84 = 12B + 12C + 12B - 12C.

Simplifying the equation, we have: 204 = 24B.

Dividing both sides of the equation by 24, we find: B = 8.5 km/h.

Now, we can substitute the value of B into one of the original equations to find the value of C. Let's use Equation 1:

30 = (8.5 + C) × 3.

Simplifying the equation, we have: 30 = 25.5 + 3C.

Subtracting 25.5 from both sides of the equation, we find: 4.5 = 3C.

Dividing both sides of the equation by 3, we find: C = 1.5 km/h.

Answer

Therefore, the speed of the river's current is 1.5 km/h and the speed of the boat is 8.5 km/h.