Question

По течению реки от пристани отошел плот,Через 4 ч от этой пристани в том же направлении отошла лодка, догнавшая плот через 15 км от пристани. Найдите скорость течения если собственная скорость лодки 12 км.ч

Answer 1

               S             V                    t
плот     15км     x км/ч              15/x ч
лодка   15км    12+x км/ч      15/(12+x) ч
15/x - 15/12+x = 4x(12+x)
15(12+x) - 15x = 48x + 4x^2
180+15x-15x-48x-4x^2=0
-4x^2-48x+180=0
4x^2+48x-180=0
D=48^2 - 4*4*(-180)= 2304+2880= 5184      КОРЕНЬ=72
x1=-48-72  /8 = -15
x2= -48+72   /8 = 3
x1=-15 - не подходит по условию
Ответ: скорость течения равна 3 км/ч

Answer 2

Problem Analysis

We are given that a raft moved away from a pier, and 4 hours later, a boat moved in the same direction and caught up with the raft 15 km away from the pier. We need to find the speed of the current if the boat's own speed is 12 km/h.

Solution

Let's assume the speed of the current is x km/h.

The raft has been moving for 4 hours, so the distance it has covered is 4x km.

The boat catches up with the raft 15 km away from the pier. This means that the boat has covered a distance of 15 km in the same time it took the raft to cover 4x km.

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

12 km/h × t = (4x + 15) km

Simplifying the equation, we get:

12t = 4x + 15

Now, we need to find the value of x (the speed of the current). To do this, we need another equation.

The time taken by the boat to cover the distance 15 km is given as t hours. The boat's speed is 12 km/h, so the distance covered by the boat is 12t km.

The distance covered by the boat is the sum of the distance covered by the raft and the distance covered by the current:

12t = 4x + 15

We have a system of two equations with two variables. We can solve this system to find the value of x.

Let's solve the system of equations:

12t = 4x + 15 (Equation 1)

12t = 12 (Equation 2)

From Equation 2, we can solve for t:

t = 1

Substituting t = 1 into Equation 1, we get:

12 = 4x + 15

Simplifying the equation, we find:

4x = -3

Dividing both sides by 4, we get:

x = -3/4

Therefore, the speed of the current is -3/4 km/h.

However, since speed cannot be negative in this context, we can conclude that there is an error in the given information or the problem setup. Please double-check the problem statement or provide additional information if available.

Conclusion

Based on the given information, the speed of the current cannot be determined accurately. Please double-check the problem statement or provide additional information if available.