Question

Моторная лодка прошла против течения 24 км и вернулась обратно, затратив на обратный путь на 20 мин меньше, чем при движении против течения. Найдите скорость в (км/ч) лодки в неподвижной воде, если скорость течения равна 3 км/ч.

Answer 1

 24  -      24    = 20 мин(или 1\3)
х-3        х+3

72х +216  -72х +216  = х^2- 9
432 - x^2 +9 =0
x^2= 441
x=21 км\час

Answer 2

Problem Analysis

We are given that a motorboat traveled 24 km against a current and then returned back, spending 20 minutes less on the return journey compared to the journey against the current. We need to find the speed of the boat in still water, given that the current speed is 3 km/h.

Solution

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the speed of the boat against the current is (x - 3) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the speed of the boat with the current is (x + 3) km/h.

We are given that the boat traveled 24 km against the current and spent 20 minutes less on the return journey. Let's calculate the time taken for each leg of the journey.

The time taken to travel 24 km against the current is given by: time against current = distance / speed against current = 24 / (x - 3)

The time taken to travel 24 km with the current is given by: time with current = distance / speed with current = 24 / (x + 3)

We are also given that the time taken for the return journey is 20 minutes less than the time taken for the journey against the current. So, we can write the following equation:

time against current - time with current = 20 minutes

Converting 20 minutes to hours, we have: time against current - time with current = 20 / 60 hours

Now, let's substitute the expressions for time against current and time with current into the equation and solve for x.

Calculation

Substituting the expressions for time against current and time with current into the equation, we have:

(24 / (x - 3)) - (24 / (x + 3)) = 20 / 60

Simplifying the equation, we get:

(24(x + 3) - 24(x - 3)) / ((x - 3)(x + 3)) = 1/3

Expanding and simplifying further, we have:

(24x + 72 - 24x + 72) / (x^2 - 9) = 1/3

Simplifying the numerator, we get:

144 / (x^2 - 9) = 1/3

Cross-multiplying, we have:

3 * 144 = x^2 - 9

Simplifying further, we get:

432 = x^2 - 9

Adding 9 to both sides, we have:

x^2 = 441

Taking the square root of both sides, we have:

x = 21

Therefore, the speed of the boat in still water is 21 km/h.

Answer

The speed of the boat in still water is 21 km/h.