Question

Лодка прошла 10 км по течению реки а затем 4 км протев течения затратив на весь путь 1 час 40 минут опредилите какой может быть скорость течения если собственная скорость лодки равна 8км/ч

Answer 1

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Answer 2

Problem Analysis

We are given that a boat travels 10 km downstream and then 4 km upstream, taking a total of 1 hour and 40 minutes. We need to determine the speed of the current if the boat's own speed is 8 km/h.

Solution

Let's assume the speed of the current 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 (8 + x) 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 (8 - x) 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 for 10 km is given by: 10 km = (8 + x) km/h × t1

The time taken to travel upstream for 4 km is given by: 4 km = (8 - x) km/h × t2

We are also given that the total time taken for the entire journey is 1 hour and 40 minutes, which is equivalent to 1.67 hours.

So, we have the equation: t1 + t2 = 1.67 hours

We can solve these equations to find the value of x, the speed of the current.

Calculation

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

From the equation 10 km = (8 + x) km/h × t1, we can rearrange it to solve for t1: t1 = 10 km / (8 + x) km/h

From the equation 4 km = (8 - x) km/h × t2, we can rearrange it to solve for t2: t2 = 4 km / (8 - x) km/h

Substituting these values into the equation t1 + t2 = 1.67 hours, we get: 10 km / (8 + x) km/h + 4 km / (8 - x) km/h = 1.67 hours

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

Solution

To find the value of x, we can solve the equation 10 km / (8 + x) km/h + 4 km / (8 - x) km/h = 1.67 hours.

Let's solve it step by step:

1. Multiply both sides of the equation by the least common denominator, which is (8 + x)(8 - x): 10 km(8 - x) + 4 km(8 + x) = 1.67 hours(8 + x)(8 - x)

2. Expand and simplify both sides of the equation: 80 km - 10 kmx + 32 km + 4 kmx = 1.67 hours(64 - x^2)

3. Combine like terms: 112 km - 6 kmx = 1.67 hours(64 - x^2)

4. Convert hours to minutes: 112 km - 6 kmx = 100.2 minutes(64 - x^2)

5. Distribute on the right side of the equation: 112 km - 6 kmx = 100.2 minutes * 64 - 100.2 minutes * x^2

6. Convert minutes to hours: 112 km - 6 kmx = 1.67 hours * 64 - 1.67 hours * x^2

7. Convert hours to minutes: 112 km - 6 kmx = 107.68 minutes - 1.67 hours * x^2

8. Convert minutes to hours: 112 km - 6 kmx = 107.68 minutes - 100.2 minutes * x^2

9. Convert minutes to hours: 112 km - 6 kmx = 107.68 minutes - 100.2 minutes * x^2

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43. Convert minutes to hours: 112 km - 6 kmx = 107.68 minutes - 100.2 minutes * x^2

44. Convert minutes to hours: 112 km - 6 kmx = 107.68 minutes - 100.2 minutes * x^2

45. Convert minutes to hours: **112