Question

по течению реки лодка за 5 ч проходит расстояние 30 км, а против течения за 3 ч - расстояние 9 км. какое расстояние по этой реке пройдёт плот за 2 часа?​

Answer 1

Ответ:

3 км

Пошаговое объяснение:

30/5=6 км/ч скорость по течению

9/3=3 км/ч скорость против течения

(6-3)/2=1,5 км/ч скорость течения

1,5*2=3 км пройдет плот за 2 часа

х- собственная скорость

y- скорость течения

система:

x+y=6. x=6-y. x=4,5

x-y=3 6-y-y=3. 2y=3. y=1,5

Answer 2

Problem Analysis

We are given that a boat travels a distance of 30 km downstream in 5 hours and a distance of 9 km upstream in 3 hours. We need to find the distance that a raft will travel in 2 hours.

Downstream Speed Calculation

To find the speed of the boat downstream, we can use the formula: speed = distance / time. Using the given values, we can calculate the downstream speed of the boat: - Distance downstream = 30 km - Time taken downstream = 5 hours

Therefore, the downstream speed of the boat is 30 km / 5 hours = 6 km/h.

Upstream Speed Calculation

Similarly, to find the speed of the boat upstream, we can use the same formula: speed = distance / time. Using the given values, we can calculate the upstream speed of the boat: - Distance upstream = 9 km - Time taken upstream = 3 hours

Therefore, the upstream speed of the boat is 9 km / 3 hours = 3 km/h.

Calculation of River Current Speed

Let's assume the speed of the river current is represented by x km/h.

Calculation of Boat's Speed in Still Water

The speed of the boat in still water can be calculated using the formula: boat's speed in still water = (downstream speed + upstream speed) / 2. Using the values we calculated earlier, we can find the boat's speed in still water: - Downstream speed = 6 km/h - Upstream speed = 3 km/h

Therefore, the boat's speed in still water is (6 km/h + 3 km/h) / 2 = 4.5 km/h.

Calculation of River Current Speed

The speed of the river current can be calculated using the formula: river current speed = (downstream speed - upstream speed) / 2. Using the values we calculated earlier, we can find the river current speed: - Downstream speed = 6 km/h - Upstream speed = 3 km/h

Therefore, the river current speed is (6 km/h - 3 km/h) / 2 = 1.5 km/h.

Calculation of Raft's Speed

The speed of the raft can be calculated using the formula: raft's speed = boat's speed in still water - river current speed. Using the values we calculated earlier, we can find the raft's speed: - Boat's speed in still water = 4.5 km/h - River current speed = 1.5 km/h

Therefore, the raft's speed is 4.5 km/h - 1.5 km/h = 3 km/h.

Calculation of Distance Traveled by the Raft

To find the distance traveled by the raft in 2 hours, we can use the formula: distance = speed * time. Using the values we calculated earlier, we can find the distance traveled by the raft: - Raft's speed = 3 km/h - Time taken by the raft = 2 hours

Therefore, the distance traveled by the raft is 3 km/h * 2 hours = 6 km.

Answer

The raft will travel a distance of 6 km in 2 hours.

Conclusion

In conclusion, the raft will travel a distance of 6 km in 2 hours along the river.