Question

Моторная лодка прошла против течения реки 72 км и вернулась в пункт отправления, затратив на обратный путь на 6 часов меньше, чем на путь против течения. Найдите скорость лодки в неподвижной воде, если скорость течения равна 3 км/ч. Ответ дайте в км/ч.

Answer 1

Ясно, что при движении по течению реки скорость лодки увеличивается на скорость течения, а при движении против течения - на ту же величину уменьшается.
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 Пусть собственная скорость лодки х км/ч,
тогда по течению она плыла со скоростью х+3 км/ч,
а против течениях-3 км/ч 
Расстояние в оба конца - одно и то же.
Против течения лодка плыла 72:(х-3) часов 
По течению - 72:(х+3),
 и это время на 6 часов меньше первого.
72:(х-3) - 72:(х+3)=6 
Раскрыв скобки и приведя подобные члены, получим уравнение 
6х²=486 
х²=81 
х=9 км/ч 
Ответ:скорость лодки в неподвижной воде 9 км/ч

Answer 2

Problem Analysis

We are given that a motorboat traveled against the current of a river for 72 km and then returned to the starting point, taking 6 hours less for the return trip compared to the trip against the current. We are also given that the speed of the current is 3 km/h. We need to find the speed of the boat in still water.

Solution

Let's assume the speed of the boat in still water is V km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the speed of the boat against the current is V - 3 km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the speed of the boat with the current is V + 3 km/h.

We can use the formula speed = distance / time to calculate the time taken for each leg of the journey.

The time taken for the trip against the current is given by: t1 = 72 / (V - 3)

The time taken for the return trip with the current is given by: t2 = 72 / (V + 3)

We are given that the return trip took 6 hours less than the trip against the current. So, we can set up the equation: t1 - t2 = 6

Now, let's solve this equation to find the value of V.

Calculation

Using the equation t1 - t2 = 6, we can substitute the values of t1 and t2: (72 / (V - 3)) - (72 / (V + 3)) = 6

To simplify the equation, we can multiply both sides by (V - 3)(V + 3): 72(V + 3) - 72(V - 3) = 6(V - 3)(V + 3)

Simplifying further: 72V + 216 - 72V + 216 = 6(V^2 - 9)

Combining like terms: 432 = 6V^2 - 54

Rearranging the equation: 6V^2 = 486

Dividing both sides by 6: V^2 = 81

Taking the square root of