Question

Катер прошел 36 км по течению и 60 км по озеру, затратив на весь путь 5 ч. Скорость течения реки равна 2 км/ч. Найдите скорость катера по течению.​

Answer 1

Ответ:

≈20,5 км/ч.

Объяснение:

Пусть собственная скорость катера х км/ч, тогда его скорость по течению х+2 км/ч.

36/(х+2) + 60/х = 5

36х+60х+120-5х²-10х=0

5х²-86х-120=0

х=(86±√(7396+2400))/10=(86±√9796)/10≈(86±99)/10

х≈-1,3 (не подходит)  х≈18,5

Скорость катера по течению ≈18,5+2≈20,5 км/ч.

Answer 2

Problem Analysis

We are given that a boat traveled 36 km upstream and 60 km downstream, taking a total of 5 hours for the entire journey. The speed of the river current is given as 2 km/h. We need to find the speed of the boat in still water.

Solution

Let's assume the speed of the boat in still water is v km/h.

When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the current. So, the boat's speed relative to the ground is (v - 2) km/h.

When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. So, the boat's speed relative to the ground is (v + 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 36 km upstream is given by: 36 = (v - 2) × t1 The time taken to travel 60 km downstream is given by: 60 = (v + 2) × t2 We also know that the total time for the journey is 5 hours: t1 + t2 = 5 We can solve this system of equations to find the value of v.

Calculation

Let's solve the system of equations and.

From equation 36 = (v - 2) × t1

From equation 60 = (v + 2) × t2

From equation t1 + t2 = 5

We can rewrite equation as: t1 = 36 / (v - 2)

We can rewrite equation as: t2 = 60 / (v + 2)

Substituting the values of t1 and t2 in equation 36 / (v - 2) + 60 / (v + 2) = 5

To solve this equation, we can multiply through by (v - 2)(v + 2) to eliminate the denominators: 36(v + 2) + 60(v - 2) = 5(v - 2)(v + 2)

Expanding and simplifying: 36v + 72 + 60v - 120 = 5(v^2 - 4)

Simplifying further: 96v - 48 = 5v^2 - 20

Rearranging the equation: 5v^2 - 96v + 68 = 0

We can solve this quadratic equation using the quadratic formula: v = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 5, b = -96, and c = 68.

Substituting the values into the quadratic formula: v = (-(-96) ± √((-96)^2 - 4 * 5 * 68)) / (2 * 5)

Simplifying: v = (96 ± √(9216 - 1360)) / 10

v = (96 ± √7856) / 10

Calculating the square root of 7856: √7856 ≈ 88.57

Substituting the value into the equation: v = (96 ± 88.57) / 10

We have two possible solutions: 1. v = (96 + 88.57) / 10 ≈ 18.86 2. v = (96 - 88.57) / 10 ≈ 7.43

Since the speed of the boat cannot be negative, the speed of the boat in still water is approximately 18.86 km/h.

Answer

The speed of the boat in still water is approximately 18.86 km/h.