Question

Пограничный катер во время своего дежурства прошел по реке 105 км . При этом по течению реки он шел 4 ч , а против течения 5 ч. Найдите собственную скорость катера , если скорость течения реки равна 3 км\ч

Answer 1

Пусть х - скорость катера, тогда
4(х+3)=5 (х-3)
х=27 

Answer 2

Calculation of the Boat's Speed

To find the boat's speed, we need to consider the time it took for the boat to travel both downstream and upstream.

Given information: - Distance traveled: 105 km - Time traveled downstream: 4 hours - Time traveled upstream: 5 hours - Speed of the river current: 3 km/h

Let's calculate the boat's speed.

1. Downstream Speed: - When the boat is traveling downstream, its speed is increased by the speed of the river current. - Let's assume the boat's speed is x km/h. - The effective speed of the boat downstream is the sum of the boat's speed and the speed of the river current: (x + 3) km/h. - Using the formula: Speed = Distance / Time, we can calculate the boat's speed downstream: - (x + 3) km/h = 105 km / 4 hours

2. Upstream Speed: - When the boat is traveling upstream, its speed is decreased by the speed of the river current. - The effective speed of the boat upstream is the difference between the boat's speed and the speed of the river current: (x - 3) km/h. - Using the formula: Speed = Distance / Time, we can calculate the boat's speed upstream: - (x - 3) km/h = 105 km / 5 hours

Now, let's solve the equations to find the boat's speed.

Solving the Equations

1. Downstream Speed: - (x + 3) km/h = 105 km / 4 hours - x + 3 = 105 / 4 - x + 3 = 26.25 - x = 26.25 - 3 - x = 23.25 km/h

2. Upstream Speed: - (x - 3) km/h = 105 km / 5 hours - x - 3 = 105 / 5 - x - 3 = 21 - x = 21 + 3 - x = 24 km/h

Conclusion

The boat's speed is 23.25 km/h downstream and 24 km/h upstream.