Question

Теплоход проходит расстояние между А и Б по реке за 5 суток, а обратно за 7 часов. За сколько прошел бы это расстояние плот? Помогите, пожалуйста

Answer 1

5 суток туда и 7 часов обратно? сомневаюсь. перепроверь условие.
Будем считать, что туда 5 часов, обратно 7.
В таком случае:
S=(v+v1)t1
S=(v-v1)t2
vt1+v1t1=vt2-v1t2
v1(t1+t2)=v(t2-t1)
v1=v(t2-t1)/(t1+t2)

Answer 2

Problem Analysis

We are given that a boat travels a distance between points A and B on a river in 5 days, and returns the same distance in 7 hours. We need to determine how long it would take for a raft to cover the same distance.

Solution

To solve this problem, we can use the concept of relative speed. The boat's speed relative to the water is the same in both directions, but the current affects the boat's speed. Let's assume the boat's speed relative to the water is x and the speed of the current is y.

When the boat is traveling downstream (from A to B), the effective speed is the sum of the boat's speed and the current's speed. So the effective speed is (x + y).

When the boat is traveling upstream (from B to A), the effective speed is the difference between the boat's speed and the current's speed. So the effective speed is (x - y).

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

1. Distance downstream = Distance upstream 2. Time downstream = 5 days 3. Time upstream = 7 hours

Let's solve these equations to find the values of x and y.

Calculation

1. Distance downstream = Distance upstream - Let the distance between A and B be d. - Distance downstream = (x + y) * 5 - Distance upstream = (x - y) * (7/24) (since 7 hours is equivalent to 7/24 days) - Equating the distances: (x + y) * 5 = (x - y) * (7/24) - Simplifying the equation: 5x + 5y = (7/24)x - (7/24)y - Rearranging the equation: (5 - 7/24)x = (7/24 + 5)y - Simplifying further: (103/24)x = (167/24)y - Dividing both sides by (167/24)y: x = (167/103)y

2. Time downstream = 5 days - Time downstream = 5 - Time upstream = 7/24 - Equating the times: (d / (x + y)) = 5 and (d / (x - y)) = (7/24) - Substituting the value of x from the previous equation: (d / ((167/103)y + y)) = 5 - Simplifying the equation: (d / ((167/103 + 1)y)) = 5 - Rearranging the equation: (d / ((167/103 + 103/103)y)) = 5 - Simplifying further: (d / ((270/103)y)) = 5 - Multiplying both sides by ((270/103)y): d = 5 * ((270/103)y) - Simplifying further: d = (1350/103)y

Now, we have two equations: - x = (167/103)y - d = (1350/103)y

We need to find the time it would take for a raft to cover the same distance. Let's denote the speed of the raft as r.

The time taken by the raft to cover the distance d is given by: Time = d / r

Substituting the value of d from the equation above, we get: Time = ((1350/103)y) / r

To find the value of r, we need to find the value of y. Let's solve the equations to find y.

Solving for y

To solve for y, we can substitute the value of x from the equation x = (167/103)y into the equation 5x + 5y = (7/24)x - (7/24)y.

Let's solve this equation to find the value of y.

5 * (167/103)y + 5y = (7/24) * (167/103)y - (7/24)y

Simplifying the equation:

(835/103)y + 5y = (7/24) * (167/103)y - (7/24)y

(835/103 + 120/24)y = (7/24) * (167/103)y

(835/103 + 120/24)y = (7/24) * (167/103)y

Multiplying both sides by (103/167):

(835/103 + 120/24)y * (103/167) = (7/24) * (167/103)y * (103/167)

Simplifying the equation:

(835 + 515)y = (7/24) * (167)y

1350y = (7/24) * (167)y

Dividing both sides by y:

1350 = (7/24) * 167

Simplifying the equation:

1350 = (7/24) * 167

Now, we can solve for y:

y = (1350 / ((7/24) * 167))

Simplifying the equation:

y = (1350 / (7 * 167 / 24))

y = (1350 * 24) / (7 * 167)

y = 5400 / 1169

y ≈ 4.62

Now that we have the value of y, we can find the value of r:

r = x - y

Substituting the value of x from the equation x = (167/103)y:

r = (167/103)y - y

r = (167/103 - 103/103)y

r = (64/103)y

Substituting the value of y:

r = (64/103) * 4.62

r ≈ 2.86

Therefore, it would take approximately 2.86 hours for the raft to cover the same distance.

Answer

The raft would take approximately 2.86 hours to cover the same distance between points A and B on the river.

Please note that the above calculations are based on the assumptions made and the given information.