Question

Лодка прошла 8 км на против течения реки и 12 км по течению реки,затратив на весь путь 2 часа. Найдите скорость лодки,если скорость течения равна 2км/ч.

Answer 1

Пусть скорость лодки - х.  ⇒
8/(x-2)+12/(x+2)=2
8x+16+12x-24=2(x²-4)
20x-8=2x²-8
2x²-20x=0  I÷2
x²-10x=0
x(x-10)=0
x₁=0  x₁∉   x₂=10
Ответ: скорость лодки 10 км/ч.
 

Answer 2

Problem Analysis

We are given that a boat traveled 8 km against the current of a river and 12 km with the current of the river. The total time taken for the entire journey was 2 hours. We need to find the speed of the boat, given that the speed of the current is 2 km/h.

Solution

Let's assume the speed of the boat is B km/h. Since the boat is traveling against the current, its effective speed will be the difference between its speed and the speed of the current. Therefore, the effective speed of the boat while traveling against the current is (B - 2) km/h.

Similarly, when the boat is traveling with the current, its effective speed will be the sum of its speed and the speed of the current. Therefore, the effective speed of the boat while traveling with the current is (B + 2) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

The time taken to travel 8 km against the current is given by: 8 = (B - 2) × t1 The time taken to travel 12 km with the current is given by: 12 = (B + 2) × t2 We are also given that the total time taken for the entire journey is 2 hours: t1 + t2 = 2 We can solve this system of equations to find the value of B, the speed of the boat.

Calculation

Let's solve the system of equations:

From equation 1, we have: 8 = (B - 2) × t1

From equation 2, we have: 12 = (B + 2) × t2

From equation 3, we have: t1 + t2 = 2

We can rewrite equation 3 as: t1 = 2 - t2

Substituting this value of t1 in equation 1, we get: 8 = (B - 2) × (2 - t2)

Expanding the equation, we have: 8 = 2B - 4 - Bt2 + 2t2

Simplifying the equation, we get: Bt2 - 2t2 = 2B - 12

Factoring out B from the left side of the equation, we have: t2(B - 2) = 2B - 12

Dividing both sides of the equation by (B - 2), we get: t2 = (2B - 12) / (B - 2)

Substituting this value of t2 in equation 3, we get: t1 = 2 - (2B - 12) / (B - 2)

Now, we can substitute the values of t1 and t2 in equation 2 to solve for B: 12 = (B + 2) × ((2B - 12) / (B - 2))

Simplifying the equation, we get: 12(B - 2) = (B + 2)(2B - 12)

Expanding the equation, we have: 12B - 24 = 2B^2 - 8B - 24

Simplifying the equation further, we get: 2B^2 - 20B = 0

Factoring out 2B from the equation, we have: 2B(B - 10) = 0

Therefore, we have two possible solutions: 1. B = 0 (which is not possible in this context) 2. B - 10 = 0, which implies B = 10

Answer

The speed of the boat is 10 km/h.