Question

Моторная лодка прошла 18 км по течению реки и вернулась обратно, затратив на весь путь 4 ч. Найдите скорость лодки, если скорость течения реки равна 6 км/ч.

Answer 1

Х км/ч - скорость лодки
х+6 км/ч - скорость по течению
х-6 км/ч - скорость против течения

18/(х+6) + 18/(х-6) =4
18(х-6+х+6)=4(х-6)(х+6)
36х=4х² - 144
4х² - 36х - 144=0
х² - 9х - 36=0
D=9²+4*36=225   (±15²)
х1=(9-15)/2= - 3 - не подходит решению
х2=(9+15)/2=12(км/ч) - скорость лодки

Answer 2

Calculating the Boat's Speed

To find the speed of the boat, we can use the formula: speed = distance / time

Given: - Distance traveled with the current = 18 km - Time taken for the entire trip = 4 hours - Speed of the river's current = 6 km/h

First, let's calculate the speed of the boat when traveling with the current.

The boat's speed when traveling with the current can be represented as: speed of boat + speed of current = speed of boat with the current

Using the given values: speed of boat + 6 = 18 / t1 (where t1 is the time taken to travel downstream)

Now, let's calculate the boat's speed when traveling against the current.

The boat's speed when traveling against the current can be represented as: speed of boat - speed of current = speed of boat against the current

Using the given values: speed of boat - 6 = 18 / t2 (where t2 is the time taken to travel upstream)

We can then solve these equations to find the speed of the boat.

Calculating the Boat's Speed with the Current

Using the given values, we can calculate the boat's speed when traveling with the current: speed of boat + 6 = 18 / t1

From Source it is mentioned that the boat traveled 18 km downstream.

Calculating the Boat's Speed against the Current

Similarly, using the given values, we can calculate the boat's speed when traveling against the current: speed of boat - 6 = 18 / t2

From Source it is mentioned that the boat traveled 18 km upstream.

Solving for the Boat's Speed

We have two equations: 1. speed of boat + 6 = 18 / t1 2. speed of boat - 6 = 18 / t2

We can solve these equations to find the speed of the boat.

By adding the two equations, we get: (speed of boat + 6) + (speed of boat - 6) = (18 / t1) + (18 / t2)

Solving further, we get: 2 * speed of boat = 18 / t1 + 18 / t2

Finally, we can solve for the boat's speed: speed of boat = (18 / t1 + 18 / t2) / 2

By substituting the values of t1 and t2, we can find the speed of the boat.