Question

Моторная лодка прошла от одной пристани до другой,расстояние между которыми по реке равно 16 км,сделала стоянку на 40 мин и вернулась обратно через 3 2/3 ч после начала поездки.Найдите скорость течения реки,если известно,что скорость моторной лодки в стоячей воде равна 12 км/ч

Answer 1

40 мин=2/3 часа
х-скорость течения
12+х по течению
12-х против
16/(12+x)+16/(12-x)=3
12*32=144*3-3x^2
3x^2=3*(144-32*4)
x^2=16
x=4.
Ответ: 4 км в час.

Answer 2

Problem Analysis

We are given the following information: - The distance between two docks along the river is 16 km. - The motorboat made a 40-minute stop at the second dock. - The motorboat returned back to the first dock 3 2/3 hours after the start of the trip. - The speed of the motorboat in still water is 12 km/h.

We need to find the speed of the river's current.

Solution

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

When the motorboat is traveling downstream (from the first dock to the second dock), the effective speed of the motorboat is the sum of its speed in still water and the speed of the current. Therefore, the effective speed is (12 + x) km/h.

When the motorboat is traveling upstream (from the second dock to the first dock), the effective speed of the motorboat is the difference between its speed in still water and the speed of the current. Therefore, the effective speed is (12 - x) km/h.

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

Let's calculate the time taken for the downstream trip first: - Distance = 16 km - Speed = (12 + x) km/h - Time = Distance / Speed

Next, let's calculate the time taken for the upstream trip: - Distance = 16 km - Speed = (12 - x) km/h - Time = Distance / Speed

Finally, we can calculate the total time for the round trip by adding the time taken for the downstream trip, the time taken for the upstream trip, and the 40-minute stop: - Total Time = Downstream Time + Upstream Time + 40 minutes

We know that the total time for the round trip is 3 2/3 hours (or 3.67 hours). We can set up the equation:

Total Time = Downstream Time + Upstream Time + 40 minutes

Let's solve this equation to find the value of x, which represents the speed of the river's current.

Calculation

Let's calculate the time taken for the downstream trip first: - Distance = 16 km - Speed = (12 + x) km/h - Time = Distance / Speed

Time taken for the downstream trip = 16 / (12 + x) hours

Next, let's calculate the time taken for the upstream trip: - Distance = 16 km - Speed = (12 - x) km/h - Time = Distance / Speed

Time taken for the upstream trip = 16 / (12 - x) hours

Now, let's calculate the total time for the round trip: - Total Time = Downstream Time + Upstream Time + 40 minutes

Total Time = 16 / (12 + x) + 16 / (12 - x) + 40 minutes

Since the total time is given as 3 2/3 hours (or 3.67 hours), we can convert 40 minutes to hours by dividing it by 60: Total Time = 3.67 hours

Total Time = 16 / (12 + x) + 16 / (12 - x) + 40/60 hours

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

Solution

Let's solve the equation to find the value of x.

Total Time = 16 / (12 + x) + 16 / (12 - x) + 40/60

3.67 = 16 / (12 + x) + 16 / (12 - x) + 2/3

To simplify the equation, let's multiply both sides by (12 + x)(12 - x) to eliminate the denominators:

3.67(12 + x)(12 - x) = 16(12 - x) + 16(12 + x) + 2(12 + x)(12 - x)/3

Now, let's solve the equation for x.

Calculation

Let's solve the equation to find the value of x.

3.67(12 + x)(12 - x) = 16(12 - x) + 16(12 + x) + 2(12 + x)(12 - x)/3

Expanding the equation:

3.67(144 - x^2) = 16(12 - x) + 16(12 + x) + 2(144 - x^2)/3

Distributing and simplifying:

530.28 - 3.67x^2 = 192 - 16x + 192 + 16x + (288 - 2x^2)/3

Combining like terms:

530.28 - 3.67x^2 = 384 + (288 - 2x^2)/3

Multiplying both sides by 3 to eliminate the fraction:

1590.84 - 11.01x^2 = 1152 + 288 - 2x^2

Combining like terms:

1590.84 - 11.01x^2 = 1440 - 2x^2

Subtracting 1440 from both sides:

150.84 - 11.01x^2 = -2x^2

Adding 11.01x^