Question

Помогите решить спасибо! катер проплывает по реке расстояние. между пристаними равное 48км. ,по течению за 2часа ,а против течения за 2часа. 24 мин, Какова скорость. течения. реки и какова скорость катера в стоячей воде,

Answer 1

Пусть скорость катера v км/ч, скорость течения u км/ч, тогда
(u+v) скорость катера по течению реки
(v-u) скорость против течения
2 ч 24 мин = 2 24/60=2,4 часа

(u+v)*2=48
(v-u)*2,4=48

u+v=24
v-u=20

2v=44
u+v=24

v=22 скорость катера
u=2 скорость течения

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the current and the speed of the boat in still water. We are given the distance between the piers (48 km) and the time it takes for the boat to travel downstream (2 hours) and upstream (2 hours 24 minutes).

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

Downstream Speed

When the boat is traveling downstream, it benefits from the speed of the current, so its effective speed is the sum of the speed of the boat in still water and the speed of the current. Therefore, we can write the equation:

48 km = (b + c) * 2 hours [[1]]

Upstream Speed

When the boat is traveling upstream, it has to overcome the speed of the current, so its effective speed is the difference between the speed of the boat in still water and the speed of the current. Therefore, we can write the equation:

48 km = (b - c) * (2 hours + 24 minutes) [[2]]

Now, let's solve these equations to find the values of c and b.

Solving the Equations

To solve the equations, we can use the method of substitution. We'll solve equation [[1]] for b and substitute it into equation [[2]].

From equation [[1]], we have:

(b + c) = 48 km / 2 hours [[3]]

Simplifying equation [[3]], we get:

b + c = 24 km/h [[4]]

Now, let's substitute equation [[4]] into equation [[2]]:

48 km = (24 km/h - c) * (2 hours + 24 minutes) [[5]]

Converting 2 hours 24 minutes to hours, we have:

48 km = (24 km/h - c) * (2.4 hours) [[6]]

Simplifying equation [[6]], we get:

48 km = 57.6 km - 2.4c [[7]]

Rearranging equation [[7]], we have:

2.4c = 57.6 km - 48 km [[8]]

Simplifying equation [[8]], we get:

2.4c = 9.6 km [[9]]

Dividing both sides of equation [[9]] by 2.4, we find:

c = 4 km/h [[10]]

Now that we have the value of c, we can substitute it back into equation [[4]] to find b:

b + 4 km/h = 24 km/h [[11]]

Simplifying equation [[11]], we get:

b = 20 km/h [[12]]

Answer

Therefore, the speed of the current is 4 km/h and the speed of the boat in still water is 20 km/h.

Please let me know if you need any further assistance!