Question

расстояние между двумя пристанями по реке равно 24 км. Моторная лодка прошла от одной пристани до другой, сделала стоянку на 1 час 40 мин и вернулась обратно. Все путешествие заняло 6 2/3 часа(400мин). Найдите скорость течения реки, если известно, что скорость моторной лодки в стоячей воде равна 10км/ч

Answer 1

1час 40 минут= одна целая две трети часа, значит лодка плыла 6 целых 2/3-1 целая 2/3= 5 часов.

пусть скорость теч=х, тогда скорость по теч=10+х, против теч=10-х.

24/10+х  + 24/10-х  =5

240-24х+24х+240=50х^2 +500 - 50

480=5х^2 +500

х^2=4

х=2

ответ 2 км/час

Answer 2

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Answer 3

Problem Analysis

We are given the following information: - The distance between two piers on a river is 24 km. - A motorboat traveled from one pier to the other, made a stop for 1 hour and 40 minutes, and then returned. - The total duration of the trip was 6 2/3 hours (or 400 minutes). - The speed of the motorboat in still water is 10 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.

To find the speed of the river's current, we can use the formula:

Speed of the boat downstream - Speed of the boat upstream = 2 * Speed of the river's current

Let's calculate the speed of the boat downstream and upstream.

Calculating Speed of the Boat Downstream

When the boat is traveling downstream, it gets a boost from the current, so its effective speed is increased.

The speed of the boat downstream is given by:

Speed of the boat downstream = Speed of the boat in still water + Speed of the river's current

Substituting the given values:

Speed of the boat downstream = 10 km/h + x km/h

Calculating Speed of the Boat Upstream

When the boat is traveling upstream, it has to overcome the resistance of the current, so its effective speed is decreased.

The speed of the boat upstream is given by:

Speed of the boat upstream = Speed of the boat in still water - Speed of the river's current

Substituting the given values:

Speed of the boat upstream = 10 km/h - x km/h

Calculating the Time Taken for Each Leg of the Trip

We know that the total duration of the trip was 6 2/3 hours (or 400 minutes).

Let's assume the time taken for the downstream leg of the trip is t1 and the time taken for the upstream leg of the trip is t2.

The time taken for the downstream leg of the trip is given by:

Time taken downstream = Distance / Speed of the boat downstream

Substituting the given values:

t1 = 24 km / (10 km/h + x km/h)

The time taken for the upstream leg of the trip is given by:

Time taken upstream = Distance / Speed of the boat upstream

Substituting the given values:

t2 = 24 km / (10 km/h - x km/h)

Calculating the Total Duration of the Trip

The total duration of the trip is given by:

Total duration = Time taken downstream + Time taken upstream + Stoppage time

Substituting the given values:

400 minutes = t1 + t2 + 1 hour 40 minutes

Converting 1 hour 40 minutes to minutes:

400 minutes = t1 + t2 + 100 minutes

Solving the Equations

We have two equations:

1. t1 = 24 km / (10 km/h + x km/h) 2. t2 = 24 km / (10 km/h - x km/h) 3. 400 minutes = t1 + t2 + 100 minutes

We can solve these equations to find the value of x, which represents the speed of the river's current.

Let's solve these equations.

Solution Steps

1. Calculate the value of t1 using the equation t1 = 24 km / (10 km/h + x km/h). 2. Calculate the value of t2 using the equation t2 = 24 km / (10 km/h - x km/h). 3. Substitute the values of t1 and t2 into the equation 400 minutes = t1 + t2 + 100 minutes. 4. Solve the equation to find the value of x. 5. Provide the final answer for the speed of the river's current.

Let's perform the calculations step by step.

Step 1: Calculate t1

Using the equation t1 = 24 km / (10 km/h + x km/h), we can calculate the value of t1.

t1 = 24 km / (10 km/h + x km/h)

Step 2: Calculate t2

Using the equation t2 = 24 km / (10 km/h - x km/h), we can calculate the value of t2.

t2 = 24 km / (10 km/h - x km/h)

Step 3: Substitute values into the equation

Using the equation 400 minutes = t1 + t2 + 100 minutes, we can substitute the values of t1 and t2.

400 minutes = t1 + t2 + 100 minutes

Step 4: Solve the equation

Now, let's solve the equation to find the value of x.

Step 5: Provide the final answer

Finally, provide the answer for the speed of the river's current.

Please wait while I perform the calculations.