Question

Против течения реки плывет катер. Когда катер проплывал под мостом, ему встретилось плывущее бревно. через сколько времени катер догонит бревно, если туда он плыл 0,5 часа затем повернул и стал догонят бревно.

Answer 1

x -скорость катера

у -скорость течения/бревна

t-время движения бревна

S=yt - расстояние пройденное бревном

х-у -скорость катера против течения

0.5 часа -время против течения

0.5(x-y) -расстояние катера против течения

х+у -скорость катера по течению

t-0.5 часа -время по течению

(t-0.5)(x+y)  -расстояние катера по течению

S1=(t-0.5)(x+y)+0.5(x-y) - расстояние пройденное катером (способ1)

S1= yt+2*0.5(x-y) - расстояние пройденное катером (способ2)

приравняем правые части

(t-0.5)(x+y)+0.5(x-y) =yt+2*0.5(x-y)

(t-0.5)(x+y)-0.5(x-y) =yt

xt+yt-0.5x-0.5y-0.5x+0.5y=yt

xt-x=0

x(t-1)=0

t=1 час

Ответ 1 час

Answer 2

Problem Analysis

We are given a scenario where a boat is traveling against the current of a river. While passing under a bridge, the boat encounters a floating log. We need to determine how long it will take for the boat to catch up to the log after the boat has been traveling for 0.5 hours in one direction and then turns around to catch up to the log.

Solution

To solve this problem, we need to consider the relative speeds of the boat and the log. Let's assume that the speed of the boat in still water is B and the speed of the current is C. Since the boat is traveling against the current, its effective speed is reduced by the speed of the current, so the boat's speed is B - C.

When the boat turns around to catch up to the log, it will now be traveling with the current. In this case, the effective speed of the boat will be increased by the speed of the current, so the boat's speed is B + C.

Let's denote the distance between the boat and the log as D. When the boat is traveling against the current, it covers a distance of 0.5 * (B - C) in 0.5 hours. After turning around, the boat will cover the same distance of D in t hours, where t is the time it takes for the boat to catch up to the log.

Using the formula distance = speed * time, we can set up the following equation:

0.5 * (B - C) = D (1)

After the boat turns around, it will cover the same distance D in t hours, so we can set up another equation:

t * (B + C) = D (2)

We can solve this system of equations to find the value of t.

Calculation

Let's calculate the time it takes for the boat to catch up to the log.

From equation (1), we have:

0.5 * (B - C) = D

From equation (2), we have:

t * (B + C) = D

We can rearrange equation (1) to solve for D:

D = 0.5 * (B - C)

Substituting this value of D into equation (2), we have:

t * (B + C) = 0.5 * (B - C)

Now, we can solve for t:

t = (0.5 * (B - C)) / (B + C)

Answer

The time it takes for the boat to catch up to the log is given by the equation:

t = (0.5 * (B - C)) / (B + C)

Please provide the values of B and C (the speed of the boat in still water and the speed of the current) so that we can calculate the time it takes for the boat to catch up to the log.