Question

Моторная лодка прошла 5 км по течению и 6 км против течения реки,затратив на весь путь 1 ч.Скорость течения реки равна 3 км\ч Найдите скорость лодки по течению.

Answer 1

Х- собственная скорость лодки
х+3 скор по теч
х-3 скор против теч
5/х+3 +6/х-3 =1
5(х-3)+6(х+3)=х²-9
5х-15+6х+18=х²-9
х²-5х-6х-9-18+15=0
х²-11х-12=0
Д=121+48=169=13²
х1=11-13/2 не уд усл
х2=11+13/2=12
12+3=15 км/ч скорость по течению

Answer 2

Problem Analysis

We are given that a motorboat traveled 5 km downstream (with the current) and 6 km upstream (against the current) in a total time of 1 hour. The speed of the river's current is given as 3 km/h. We need to find the speed of the boat in still water.

Solution

Let's assume the speed of the boat in still water is x km/h.

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the boat's speed downstream is (x + 3) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the boat's speed upstream is (x - 3) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

The time taken to travel downstream for 5 km is given by: 5 km = (x + 3) km/h × t1

The time taken to travel upstream for 6 km is given by: 6 km = (x - 3) km/h × t2

We are also given that the total time for the journey is 1 hour: t1 + t2 = 1 hour

We can solve this system of equations to find the value of x, the speed of the boat in still water.

Calculation

Let's solve the system of equations:

From the equation 5 km = (x + 3) km/h × t1,