Question

Папа и сын плыли на лодке против течения. В какой-то момент сын уронил за борт папину шляпу. Только через 15 мин папа заметил пропажу, быстро развернул лодку, и они поплыли по течению с той же собственной скоростью. За сколько минут они догонят шляпу?

Answer 1

лодка плывет со скоростью. V0-Vt против течения v0+Vt- по течеию

шляпа проплыла Vt/4

лодка проплыла (V0-Vt)/4

догнать шляпу. (V0-Vt+Vt)/4=V0/4

T=(v0+vt-vt)/(v0/4)=1/4=15 минут

Answer 2

Относительно воды шляпа была неподвижна, а скорость лодки относительно воды оставлась неизменна. Поэтому, если против течения лодка шла 15 минут, то и обратно она догнала шляпу через 15 минут после разворота.

Answer 3

Problem Analysis

In this problem, a father and son are traveling in a boat against the current. At some point, the son accidentally drops the father's hat overboard. The father notices the loss 15 minutes later and quickly turns the boat around. They then start traveling downstream at the same speed as before. The question is how long it will take for them to catch up to the hat.

Solution

To solve this problem, we need to consider the relative speed of the boat and the hat. When the boat is traveling against the current, the speed of the boat relative to the hat is the sum of the boat's speed and the speed of the current. When the boat is traveling downstream, the speed of the boat relative to the hat is the difference between the boat's speed and the speed of the current.

Let's assume that the speed of the boat is B and the speed of the current is C. When the boat is traveling against the current, the relative speed of the boat and the hat is B + C. When the boat is traveling downstream, the relative speed of the boat and the hat is B - C.

Since the boat and the hat are traveling the same distance, we can set up the following equation:

Distance = Speed × Time

When the boat is traveling against the current, the distance traveled by the boat is (B + C) × 15 minutes. When the boat is traveling downstream, the distance traveled by the boat is (B - C) × T minutes, where T is the time it takes for the boat to catch up to the hat.

Setting these two distances equal to each other, we get:

(B + C) × 15 = (B - C) × T

Simplifying the equation, we have:

15B + 15C = BT - CT

Rearranging the equation, we get:

BT - 15B = 15C + CT

Factoring out B and C, we have:

B(T - 15) = C(T + 15)

Dividing both sides of the equation by (T + 15), we get:

B = (C(T + 15))/(T - 15)

Now, we can solve for T by substituting the given values of B and C.