Question

2. Моторная лодка прошла 60 км по течению реки и 36 км по озеру, затратив на весь путь 5 часов. Найдите скорость лодки по течению, если скорость течения реки равна 2 км/ч.

Answer 1

Ответ:18км/ч

Объяснение:пусть х км/ч это скорость лодки

скорость по течению реки (х+2)

скорость по озеру хх

60/(х+2) это время движения по реке

36/х по озеру

60/(х+2)+36/=5

Answer 2

Ответ:

x- собственная скорость лодки

х+2 -скорость по течению

60/(х+2)+36/х=5

60х+36(х+2)=5х(х+2)

60х+36х+72=5х²+10х

5х²-86х-72=0; D=7396+1440=8836;

x1=(86-94)/10=-8/10

x2=(86+94)/10=18(км/ч)

Ответ:сеорость по течению реки - 20 км/ч

Answer 3

Problem Analysis

We are given that a motorboat traveled 60 km upstream (against the current) on a river and then 36 km downstream (with the current) on a lake. The total time taken for the entire journey was 5 hours. We need to find the speed of the boat relative to the current.

Solution

Let's assume the speed of the boat in still water is x km/h and the speed of the current is 2 km/h.

When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the current. So, the boat's speed relative to the ground is (x - 2) km/h.

When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. So, the boat's speed relative to the ground is (x + 2) km/h.

We are given that the boat traveled 60 km upstream and 36 km downstream, taking a total of 5 hours. We can set up the following equation based on the time and distance traveled:

60 / (x - 2) + 36 / (x + 2) = 5

To solve this equation, we can multiply both sides by (x - 2)(x + 2) to eliminate the denominators:

60(x + 2) + 36(x - 2) = 5(x - 2)(x + 2)

Simplifying the equation:

60x + 120 + 36x - 72 = 5(x^2 - 4)

96x + 48 = 5x^2 - 20

Rearranging the equation:

5x^2 - 96x - 68 = 0

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