Question

Відомо, що для подолання 162 км у стоячій воді те- плоходу потрібно на 3 год більше, ніж для подолан-ня 72 км проти течії річки. Туристи подолали на цьо-му теплоході 60 км проти течії цієї річки і 54 км в сто-ячій воді за 4 год 30 хв. 1) Чому дорівнює власна швид-кість теплохода? 2) Скільки часу знадобиться турис-там, щоб подолати цією самою річкою 27 км на плоту?​

Answer 1

Объяснение:

4 часа 30 минут=4,5 часа.

Пусть скорость теплохода = х км/ч, а скорость течения реки -у км/ч. ⇒

$\left \{ {{\frac{162}{x}-\frac{72}{x-y}=3 } \atop {\frac{60}{x-y}+\frac{54}{x} =4,5 }} \right. .$

Пусть 12/(x-y)=t,  54/x=v.     ⇒

$\left \{ {{3v-6t=3\ |;3} \atop {5t+v=4,5}} \right. \ \ \ \ \left \{ {{v-2t=1} \atop {5t+v=4,5}} .\right.$

Вычитаем из второго уравнения первое:

$7t=3,5\ |:7\\t=0,5\ \ \ \ \Rightarrow\\\frac{12}{x-y}=0,5\ |:2\\x-y=24.\\ v-2*0,5=1\\v-1=1\\v=2\\\frac{54}{x}=2\ |:2\\\frac{27}{x}=1\\x=27\ \ \ \ \Rightarrow\\27-y=24\\y=3.$

Ответ: скорость теплохода 27 км/ч, скорость течения реки 3 км/ч.

Answer 2

Answer:

1) To find the speed of the boat, we can use the formula: speed = distance / time. Let's calculate the speed for both scenarios:

- For the 162 km distance in still water, it takes 3 hours longer than the 72 km distance against the current. Let's assume the speed in still water is x km/h. So, the time taken to cover 162 km in still water would be (162 / x) hours, and the time taken to cover 72 km against the current would be (72 / x) hours + 3 hours.

- From the given information, we know that the tourists covered 60 km against the current in 4 hours and 30 minutes (which is 4.5 hours), and they covered 54 km in still water in 4 hours and 30 minutes (which is also 4.5 hours).

Now, we can set up the following equations:

(162 / x) = (72 / x) + 3 (Equation 1)

(60 / (x - y)) = 4.5 (Equation 2)

(54 / (x + y)) = 4.5 (Equation 3)

Where y represents the speed of the current.

To solve these equations, we can use substitution or elimination methods. Let's use the substitution method:

From Equation 2, we can express y in terms of x:

(60 / (x - y)) = 4.5

(x - y) = 60 / 4.5

(x - y) = 40/3 (Equation 4)

From Equation 3, we can express y in terms of x:

(54 / (x + y)) = 4.5

(x + y) = 54 / 4.5

(x + y) = 12 (Equation 5)

Now, we can substitute Equation 4 and Equation 5 into Equation 1:

(162 / x) = (72 / x) + 3

162 = 72 + 3x

3x = 162 - 72

3x = 90

x = 30

Therefore, the speed of the boat in still water is 30 km/h.

2) To find the time it will take for the tourists to cover 27 km on a raft, we need to consider the speed of the current. Let's assume the speed of the current is y km/h.

Using the formula speed = distance / time, we can set up the following equation:

(27 / (x + y)) = t (Equation 6)

Where t represents the time taken to cover 27 km on a raft.

We already know the speed of the boat in still water is 30 km/h (from the previous calculation).

To find the speed of the current, we can use Equation 5:

(x + y) = 12

30 + y = 12

y = 12 - 30

y = -18

Since the speed of the current cannot be negative, we can conclude that there is an error in the given information or calculations.

Therefore, we cannot determine the time it will take for the tourists to cover 27 km on a raft with the given information.

Please note that the given information may contain errors, as the speed of the current cannot be negative.