Question

Теплоход проплывает некоторое расстояние по течению реки за 10 ч против течения за 14 ч .За сколько часов такое же расстояние проплывет бревно?РЕШИТЕ НЕ УРОВНЕНИЕМ!!!!!!!!!!!!!!!!!!!!!

Answer 1

14-10=4 ч
14+10-14=20 ч

Answer 2

Problem Analysis

We are given that a boat travels a certain distance downstream in 10 hours and the same distance upstream in 14 hours. We need to determine how long it would take for a log to travel the same distance.

Solution

Let's assume that the distance traveled by the boat downstream and upstream is represented by d.

When the boat is traveling downstream, it benefits from the speed of the river, which we'll call r. So, the effective speed of the boat downstream is the sum of its own speed and the speed of the river, which we'll call b.

When the boat is traveling upstream, it has to overcome the speed of the river, so its effective speed is the difference between its own speed and the speed of the river.

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

1. Downstream speed: (b + r) = d / 102. Upstream speed: (b - r) = d / 14 To find the time it takes for the log to travel the same distance, we need to determine the speed of the log relative to the river. Since the log is not affected by the speed of the river, its effective speed is equal to its own speed, which we'll call l.

We can set up the following equation for the log's speed:

3. Log's speed: l = d / t, where t is the time it takes for the log to travel the distance.

To find the value of t, we need to solve equations and simultaneously.

Solving the Equations

Let's solve equations and to find the values of b and r:

Adding equations and:

(b + r) + (b - r) = d / 10 + d / 14

Simplifying:

2b = d / 10 + d / 14

Combining the fractions:

2b = (7d + 5d) / 70

Simplifying further:

2b = 12d / 70

Dividing both sides by 2:

b = 6d / 70

Simplifying:

b = 3d / 35 Now, let's substitute the value of b from equation into equation:

(3d / 35) + r = d / 10

Multiplying both sides by 35 to eliminate the fraction:

3d + 35r = 3.5d

Simplifying:

35r = 0.5d

Dividing both sides by 35:

r = 0.5d / 35

Simplifying further:

r = d / 70 Now, let's substitute the values of b and r from equations and into equation:

l = d / t

Substituting b = 3d / 35 and r = d / 70:

l = d / t = (3d / 35) - (d / 70)

Simplifying:

l = d / t = (6d - d) / 70

Simplifying further:

l = d / t = 5d / 70

Dividing both sides by d:

1 / t = 5 / 70

Cross-multiplying:

70 = 5t

Dividing both sides by 5:

t = 70 / 5

Simplifying:

t = 14

Therefore, it would take the log 14 hours to travel the same distance.

Answer

The log would take 14 hours to travel the same distance.