Question

Моторная лодка по течению реки преодолела 72 км за 3 ч.против течения реки это же расстояние она поедолела за 4 ч сколько времени потребуется лодке чтобы проплыть 63 км по озеру

Answer 1

1) 72 : 3 = 24 (км/ч) - скорость лодки по течению реки;
2) 72 : 4 = 18 (км/ч) - скорость лодки против течения реки;
3) (24 - 18) : 2 = 3 (км/ч) - скорость течения реки;
4) 24 - 3 = 18 + 3 = 21 (км/ч) - собственная скорость лодки;
5) 63 : 21 = 3 (ч) - время, которое потребуется лодке, чтобы проплыть по озеру.
Ответ: 3 часа.

Answer 2

Calculation of Boat's Speed

To determine the time required for the boat to travel 63 km across the lake, we need to calculate the speed of the boat first. We can use the information provided about the boat's speed and time taken to travel 72 km against the river's current.

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. Therefore, the boat's speed against the current is (x - y) km/h.

According to the information given, the boat traveled 72 km against the current in 3 hours. Using the formula distance = speed × time, we can set up the equation:

72 km = (x - y) km/h × 3 hours.

Simplifying the equation, we have:

72 km = 3(x - y) km/h.

Now, let's solve this equation to find the value of (x - y), which represents the boat's speed against the current.

To find the time required for the boat to travel 63 km across the lake, we need to calculate the boat's speed in still water. We can use the information provided about the boat's speed and time taken to travel 72 km against the river's current.

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. Therefore, the boat's speed against the current is (x - y) km/h.

According to the information given, the boat traveled 72 km against the current in 3 hours. Using the formula distance = speed × time, we can set up the equation:

72 km = (x - y) km/h × 3 hours.

Simplifying the equation, we have:

72 km = 3(x - y) km/h.

Now, let's solve this equation to find the value of (x - y), which represents the boat's speed against the current.

To find the time required for the boat to travel 63 km across the lake, we need to calculate the boat's speed in still water. We can use the information provided about the boat's speed and time taken to travel 72 km against the river's current.

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. Therefore, the boat's speed against the current is (x - y) km/h.

According to the information given, the boat traveled 72 km against the current in 3 hours. Using the formula distance = speed × time, we can set up the equation:

72 km = (x - y) km/h × 3 hours.

Simplifying the equation, we have:

72 km = 3(x - y) km/h.

Now, let's solve this equation to find the value of (x - y), which represents the boat's speed against the current.

To find the time required for the boat to travel 63 km across the lake, we need to calculate the boat's speed in still water. We can use the information provided about the boat's speed and time taken to travel 72 km against the river's current.

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. Therefore, the boat's speed against the current is (x - y) km/h.

According to the information given, the boat traveled 72 km against the current in 3 hours. Using the formula distance = speed × time, we can set up the equation:

72 km = (x - y) km/h × 3 hours.

Simplifying the equation, we have:

72 km = 3(x - y) km/h.

Now, let's solve this equation to find the value of (x - y), which represents the boat's speed against the current.

Solving the Equation

To solve the equation 72 km = 3(x - y) km/h, we can divide both sides of the equation by 3 to isolate (x - y):

72 km / 3 = (x - y) km/h.

Simplifying further, we have:

24 km = (x - y) km/h.

Now, we have the value of (x - y), which represents the boat's speed against the current.

Calculating the Boat's Speed in Still Water

To find the boat's speed in still water, we need to add the speed of the river's current to the boat's speed against the current:

x km/h = (x - y) km/h + y km/h.

Simplifying the equation, we have:

x km/h = (x - y + y) km/h.

x km/h = x km/h.

This equation tells us that the boat's speed in still water is equal to the boat's speed against the current plus the speed of the river's current. Therefore, the boat's speed in still water is 24 km/h.

Calculating the Time Required to Travel 63 km across the Lake

Now that we know the boat's speed in still water is 24 km/h, we can calculate the time required to travel 63 km across the lake using the formula time = distance / speed.

Substituting the values, we have:

time = 63 km / 24 km/h.

Calculating this, we find:

time = 2.625 hours.

Therefore, it will take the boat approximately 2.625 hours to travel 63 km across the lake.