Question

за 6 часов лодка прошла 62 км.Первые 2часа лодка шла по озеру,а остав. время -по реке против течения.Найдите скорость лодки если скорость течения 1 км/ч

Answer 1

Пусть x км/ч собственная скорость лодки,
тогда x-1 км/ч скорость ее будет против течения
2x км - прошла лодка по озеру
4(x-1) км - прошла против течения

Составим уравнение:
2x+4(x-1)=62
2x+4x-4=62
6x=66
x=11

Ответ: 11 км/ч

Answer 2

Calculation of Boat Speed

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

Speed = Distance / Time

Given that the boat traveled 62 km in 6 hours, we can calculate the speed as follows:

Speed = 62 km / 6 hours

Now, let's break down the time spent by the boat on the lake and the river.

The boat spent the first 2 hours on the lake, and the remaining time on the river against the current.

To calculate the speed of the boat, we need to consider the speed of the current as well. In this case, the speed of the current is given as 1 km/h.

Let's denote the speed of the boat as 'B' and the speed of the current as 'C'.

For the first 2 hours on the lake, the boat's speed relative to the ground is the sum of its speed and the speed of the current:

Boat's speed on the lake = B + C

For the remaining time on the river against the current, the boat's speed relative to the ground is the difference between its speed and the speed of the current:

Boat's speed on the river = B - C

Since the boat traveled a total distance of 62 km, we can set up the following equation:

2(B + C) + 4(B - C) = 62

Simplifying the equation:

2B + 2C + 4B - 4C = 62

6B - 2C = 62

Now, we have two equations:

2B + 2C = 62

6B - 2C = 62

We can solve these equations simultaneously to find the values of B and C.

Let's solve the equations:

2B + 2C = 62 (Equation 1)

6B - 2C = 62 (Equation 2)

Adding Equation 1 and Equation 2:

8B = 124

Dividing both sides by 8:

B = 15.5 km/h

Therefore, the speed of the boat is 15.5 km/h.

Please note that the speed of the current is not required to calculate the speed of the boat. It is only used to determine the boat's speed relative to the ground on the lake and the river.