Question

Теплохід пройшов 16 км по озеру, а потім 18 км по річці, яка бере початок з цього озера, за 1 годину. Знайдіть з якою швидкістю (в км / год) рухався теплохід в озері, якщо швидкість течії 4 км / год.

Answer 1

Нехай х км/год швидкисть техлохида. Тоди (х+4)км/год- швидкисть по течии рички
Складаемо ривняння:
16/х+18/(х+4)=1
х²-30х-64=0
х₁=-2 - посторонний коринь, бо вин менше 0
х₂=32
Видповидь: 32км/год

Answer 2

Problem Analysis

We are given that a boat traveled 16 km on a lake and then 18 km on a river, which originates from this lake, in a total of 1 hour. The current in the river is flowing at a speed of 4 km/h. We need to find the speed of the boat on the lake.

Solution

Let's assume the speed of the boat on the lake is x km/h.

The time taken to travel 16 km on the lake can be calculated using the formula: time = distance / speed. Therefore, the time taken to travel 16 km on the lake is 16 / x hours.

The time taken to travel 18 km on the river can also be calculated using the same formula: time = distance / speed. However, in this case, we need to consider the speed of the boat relative to the river. Since the current is flowing at a speed of 4 km/h, the effective speed of the boat on the river is (x + 4) km/h. Therefore, the time taken to travel 18 km on the river is 18 / (x + 4) hours.

According to the problem statement, the total time taken to travel both distances is 1 hour. Therefore, we can write the equation:

16 / x + 18 / (x + 4) = 1

To solve this equation, we can multiply through by x(x + 4) to eliminate the denominators:

16(x + 4) + 18x = x(x + 4)

Simplifying the equation:

16x + 64 + 18x = x^2 + 4x

34x + 64 = x^2 + 4x

x^2 - 30x - 64 = 0

Now, we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = -30, and c = -64.

Calculating the values:

x = (-(-30) ± √((-30)^2 - 4 * 1 * -64)) / (2 * 1)

x = (30 ± √(900 + 256)) / 2

x = (30 ± √1156) / 2

x = (30 ± 34) / 2

We have two possible solutions for x:

1. x = (30 + 34) / 2 = 64 / 2 = 32 2. x = (30 - 34) / 2 = -4 / 2 = -2

Since speed cannot be negative, we discard the second solution.

Therefore, the speed of the boat on the lake is 32 km/h.

Answer

The speed of the boat on the lake is 32 km/h.