Question

Расстояние между двумя пунктами по реке равно 80 км.Это расстояние лодка проплывает по течению реки 4 ч,а против течения -за 5 ч.Найдите собственную скорость лодки и скорость течения реки.

Answer 1

Система:
4(х+у)=80
5(х-у)=80

4х+4у=80   | *5        20x+20y=400     
5х-5у=80    | *4        20x=20y=320

40x =720
x=18         
4*18 +4y =80
y=2
Ответ: скорость лодки 18 км/час  скорость течения реки 2 км/час

Answer 2

Х км/ч – скорость лодки
У км/ч скорость реки
(х-у) км/ч скорость против течения
(х+у) км/ч скорость по течению
Получили сист ур
4(х+у)=80
5(х-у)=80
Решение дает х=2 км/ч скорость реки
У=18 км/ч скорость лодки

Answer 3

Calculating Boat's Speed and River's Current Speed

To find the boat's speed and the river's current speed, we can use the following formulae:

1. Let's denote the boat's speed as b and the river's current speed as c. 2. When the boat travels downstream (with the current), its effective speed is the sum of its speed and the river's current speed: b + c. 3. When the boat travels upstream (against the current), its effective speed is the difference between its speed and the river's current speed: b - c.

We are given the following information: - Distance = 80 km - Time downstream = 4 hours - Time upstream = 5 hours

Using the formula Distance = Speed × Time, we can set up the following equations:

1. 80 = (b + c) × 4 (downstream) 2. 80 = (b - c) × 5 (upstream)

Let's solve these equations to find the boat's speed and the river's current speed.

Calculations

Using the given equations, we can solve for the boat's speed and the river's current speed:

1. From the downstream equation: 80 = 4b + 4c. 2. From the upstream equation: 80 = 5b - 5c.

To solve for the boat's speed and the river's current speed, we can use the method of substitution or elimination.