Question

Катер прошел 40 км по течению реки и 6 км против течения,затратив на весь путь 3 часа. Какова собственная скорость катера,если скорость течения 2 км/ч

Answer 1

v+2(км/ч)скорость по течению

v-2(км/ч)скорость против течения

40/v+2 (ч) время движения по течению

6/v-2 (ч) время движения против течения

40/v+2+6/v-2=3 (ч) время всего пути.

Решая уравнение, получим, что собственная скорость катера (но похоже, что что-то не точно может быть 40?)

Answer 2

Problem Analysis

We are given that a boat traveled 40 km downstream and 6 km upstream in a total of 3 hours. The speed of the current is given as 2 km/h. We need to find the speed of the boat.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed downstream is (x + 2) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. So, the effective speed upstream is (x - 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 downstream is given by the equation: 40 km = (x + 2) km/h × t1 hours The time taken to travel upstream is given by the equation: 6 km = (x - 2) km/h × t2 hours We are also given that the total time taken for the entire journey is 3 hours: t1 + t2 = 3 hours We can solve this system of equations to find the value of x, which represents the speed of the boat.

Calculation

Let's solve the system of equations to find the value of x.

From equation we can rewrite it as: t1 = 40 km / (x + 2) km/h From equation we can rewrite it as: t2 = 6 km / (x - 2) km/h Substituting equations and into equation we get: 40 km / (x + 2) km/h + 6 km / (x - 2) km/h = 3 hours To solve this equation, we can multiply both sides by the least common multiple of the denominators, which is (x + 2)(x - 2).

After simplifying the equation, we get a quadratic equation: 40(x - 2) + 6(x + 2) = 3(x + 2)(x - 2)

Simplifying further, we get: 40x - 80 + 6x + 12 = 3(x^2 - 4)

Simplifying again, we get: 46x - 68 = 3x^2 - 12

Rearranging the equation, we get: 3x^2 - 46x + 80 = 0

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

For our equation, the values of a, b, and c are: a = 3, b = -46, c = 80

Substituting these values into the quadratic formula, we get: x = (-(-46) ± √((-46)^2 - 4 * 3 * 80)) / (2 * 3)

Simplifying further, we get: x = (46 ± √(2116 - 960)) / 6

Simplifying the square root, we get: x = (46 ± √1156) / 6

Taking the square root of 1156, we get: x = (46 ± 34) / 6

Simplifying further, we get two possible values for x: x = 80 / 6 = 13.33 or x = 12 / 6 = 2

Since the speed of the boat cannot be negative, we can discard the negative value of x.

Therefore, the speed of the boat is 13.33 km/h.

Answer

The speed of the boat is 13.33 km/h.