Question

Катер за 5ч движения по течению реки проходит на 70 км больше , чем за 3ч движения против течения . Найдите скорость катера в стоячей воде и скорость течения , если за 9ч движения по озеру он проходит столько , сколько за 10ч движения против течения рекиPS : с ходом решения пожалуйста

Answer 1

Х км/час  - скорость катера,  у км/час - скорость течения
(х+у) км/час - скорость по течению
(х-у) км/час - скорость против течения

$\left \{ {{5(x+y)=3(x-y)+70} \atop {9x=10(x-y)}} \right. \; \left \{ {{5x+5y=3x-3y+70} \atop {9x=10x-10y}} \right. \; \left \{ {{2x=70-8y} \atop {x=10y}} \right. \\\\2\cdot 10y=70-8y\\\\28y=70\\\\y=2,5\\\\x=25$

Answer 2

Calculating the Speed of the Boat and the Speed of the Current

To find the speed of the boat in still water and the speed of the current, we can use the following approach:

Let's denote the speed of the boat in still water as b and the speed of the current as c.

Given: - The boat travels 70 km more in 5 hours downstream than in 3 hours upstream. - In 9 hours on the lake, it travels the same distance as in 10 hours upstream on the river.

We can set up the following equations based on the given information:

1. Equation 1: - Downstream speed = (b + c) km/h - Upstream speed = (b - c) km/h - Distance downstream = 5 * (b + c) km - Distance upstream = 3 * (b - c) km - According to the given information, the boat travels 70 km more downstream than upstream: 5 * (b + c) = 3 * (b - c) + 70

2. Equation 2: - Speed in still water = b km/h - Speed of the current = c km/h - Distance on the lake = 9 * b km - Distance upstream on the river = 10 * (b - c) km - According to the given information, the distances are equal: 9 * b = 10 * (b - c)

Let's solve these equations to find the values of b and c.

Solving the Equations

Using the given equations, we can solve for the values of b and c:

1. From Equation 1: 5 * (b + c) = 3 * (b - c) + 70 5b + 5c = 3b - 3c + 70 5b - 3b + 5c + 3c = 70 2b + 8c = 70 Equation 3: 2b + 8c = 70

2. From Equation 2: 9 * b = 10 * (b - c) 9b = 10b - 10c 10c = 10b - 9b 10c = b Equation 4: 10c = b

Now, we can use Equation 4 to substitute the value of b in Equation 3 and solve for c.

Calculating the Values

Substituting the value of b from Equation 4 into Equation 3: 2 * (10c) + 8c = 70 20c + 8c = 70 28c = 70 c = 70 / 28 c = 2.5 km/h

Substituting the value of c back into Equation 4: b = 10c b = 10 * 2.5 b = 25 km/h

Conclusion

Therefore, the speed of the boat in still water is 25 km/h and the speed of the current is 2.5 km/h.