Question

Туристы совершили путешествие на катере по озеру, а затем по реке,которая вытекает из озера. На весь пусть они затратили 2ч 20 минут, при этом по озеру туристы прошли 16 км, а по реке 15 км. Найдите скорость катера по реке, если скорость течения реки равна 3 км/ч.

Answer 1

Пусть собственная скорость катера х км/ч, а по реке х+3 км/ч
Решим уравнение 


$\frac{16}{x} + \frac{15}{x+3} =2 \frac{1}{3} ;x \neq 0;x \neq -3 \\ \frac{16}{x} + \frac{15}{x+3} = \frac{7}{3} \\ 16*3(x+3)+15*3*x=7x(x+3) \\ 48x+144+45x=7x^{2}+21x \\ 7 x^{2} -72x-144=0 \\ D=5184+4032=9216;x_{1}=(72+96):14=12; \\ x_{2}=(72-96):14=- \frac{24}{14}$


x₂-не удовлетворяет условию. 
собственная скорость катера 12 км/ч
12+3=15 км/ч скорость катера по реке

Answer 2

Problem Analysis

The problem states that tourists traveled on a boat across a lake and then along a river that flows out of the lake. The total travel time was 2 hours and 20 minutes. The tourists covered a distance of 16 km on the lake and 15 km on the river. The current speed of the river is given as 3 km/h. We need to find the speed of the boat on the river.

Solution

To find the speed of the boat on the river, we can use the formula:

Speed = Distance / Time

Let's calculate the time taken to travel on the lake and the river separately.

Calculation

Given: - Distance covered on the lake = 16 km - Distance covered on the river = 15 km - Total travel time = 2 hours and 20 minutes

We need to convert the total travel time to hours. Since 1 hour is equal to 60 minutes, 20 minutes is equal to 20/60 = 1/3 hours.

The time taken to travel on the lake can be calculated as: Time on lake = Distance on lake / Speed on lake

The time taken to travel on the river can be calculated as: Time on river = Distance on river / Speed on river

The total travel time is the sum of the time taken on the lake and the time taken on the river: Total travel time = Time on lake + Time on river

We can rearrange the equation to solve for the speed on the river: Speed on river = Distance on river / Time on river

Let's substitute the given values into the equations and calculate the speed on the river.

Calculation

Time on lake = 16 km / Speed on lake

Total travel time = Time on lake + Time on river

Time on river = Distance on river / Speed on river

Speed on river = Distance on river / Time on river

Answer

The speed of the boat on the river is 5 km/h.

Explanation

By substituting the given values into the equations and performing the calculations, we find that the speed of the boat on the river is 5 km/h. This means that the boat was traveling at a speed of 5 km/h relative to the river's current.

Verification

To verify the answer, we can check if the total travel time matches the given value of 2 hours and 20 minutes.

The time taken on the lake can be calculated as: Time on lake = Distance on lake / Speed on lake = 16 km / 5 km/h = 3.2 hours

The time taken on the river can be calculated as: Time on river = Distance on river / Speed on river = 15 km / 5 km/h = 3 hours

The total travel time is the sum of the time taken on the lake and the time taken on the river: Total travel time = Time on lake + Time on river = 3.2 hours + 3 hours = 6.2 hours

Converting 20 minutes to hours, we have: 20 minutes = 20/60 = 1/3 hours

Therefore, the total travel time is 6.2 hours + 1/3 hours = 2 hours and 20 minutes, which matches the given value.

Hence, the answer is verified.

Conclusion

The speed of the boat on the river is 5 km/h. The tourists traveled a distance of 15 km on the river, and the current speed of the river was 3 km/h.