Question

По течению реки лодка за 3 часа 20 минут проходит расстояние 30 км а против течения за 4 часа расстояние 28 км Какое расстояние по озеру пройдет лодка за полтора часа

Answer 1

3:20 = 30км по течению 9 км в час
4:00 = 28км против течения 7км в час
скорость реки 1км в час

1:30 = ? 8*1,5=12 км по озеру, без течения

Answer 2

Calculation of Boat's Speed

To determine the distance the boat will travel across the lake in one and a half hours, we first need to calculate the speed of the boat in still water and the speed of 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.

According to the given information, the boat travels a distance of 30 km downstream (with the current) in 3 hours and 20 minutes, and a distance of 28 km upstream (against the current) in 4 hours.

Using the formula distance = speed × time, we can set up the following equations:

1. Downstream: (x + y) × 3.33 = 30 km (since 20 minutes is equal to 1/3 of an hour) 2. Upstream: (x - y) × 4 = 28 km

Now, let's solve these equations to find the values of x and y.

Solving the Equations

From equation 1, we can solve for x + y:

(x + y) × 3.33 = 30

Simplifying the equation:

x + y = 30 ÷ 3.33

x + y = 9

From equation 2, we can solve for x - y:

(x - y) × 4 = 28

Simplifying the equation:

x - y = 28 ÷ 4

x - y = 7

Now, we have a system of equations:

1. x + y = 9 2. x - y = 7

We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method:

Adding equation 1 and equation 2:

(x + y) + (x - y) = 9 + 7

Simplifying the equation:

2x = 16

Dividing both sides by 2:

x = 8

Substituting the value of x back into equation 1:

8 + y = 9

Simplifying the equation:

y = 9 - 8

y = 1

Therefore, the speed of the boat in still water is 8 km/h, and the speed of the river's current is 1 km/h.

Distance Traveled Across the Lake

Now that we know the speed of the boat in still water and the speed of the river's current, we can calculate the distance the boat will travel across the lake in one and a half hours.

The boat's speed across the lake can be calculated as the difference between the boat's speed in still water and the speed of the river's current:

Boat's speed across the lake = Boat's speed in still water - Speed of the river's current

Boat's speed across the lake = 8 km/h - 1 km/h

Boat's speed across the lake = 7 km/h

Using the formula distance = speed × time, we can calculate the distance the boat will travel across the lake in one and a half hours:

Distance = 7 km/h × 1.5 hours

Distance = 10.5 km

Therefore, the boat will travel a distance of 10.5 km across the lake in one and a half hours.

Please note that the calculations provided are based on the given information and assumptions made.