Question

За 8 часов по течению моторная лодка проходит расстояние в 2 раза большее чем за 5 часов против течения.Какова скорость течения, если собственная скорость лодки 13,5 км/ч

Answer 1

Х-скорость течения

8(13,5+х)=2*5(13,5-х)
4(13,5+х)=5(13,5-х)
54+4х=67,5-5х
9х=13,5
х=13,5:9=1,5 км/ч

Answer 2

Problem Analysis

We are given that a motorboat travels a distance in 8 hours that is twice as long as the distance it travels in 5 hours against the current. We need to find the speed of the current, given that the boat's own speed is 13.5 km/h.

Solution

Let's assume the speed of the current is x km/h.

When the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the distance traveled in 8 hours is given by:

Distance with current = (13.5 + x) km/h * 8 hours

When the boat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. Therefore, the distance traveled in 5 hours is given by:

Distance against current = (13.5 - x) km/h * 5 hours

According to the problem, the distance with the current is twice as long as the distance against the current. Therefore, we can write the equation:

(13.5 + x) * 8 = 2 * (13.5 - x) * 5

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

Calculation

Let's solve the equation step by step:

(13.5 + x) * 8 = 2 * (13.5 - x) * 5

Expanding the equation:

108 + 8x = 135 - 10x

Combining like terms:

18x = 27

Dividing both sides by 18:

x = 1.5

Answer

Therefore, the speed of the current is 1.5 km/h.

Verification

To verify our answer, let's substitute the value of x back into the equation and check if both sides are equal:

(13.5 + 1.5) * 8 = 2 * (13.5 - 1.5) * 5

15 * 8 = 2 * 12 * 5

120 = 120

The equation holds true, which confirms that our answer is correct.