Question

Теплоход проплыл 93 км по течению реки за 3 часа и 100 км против течения за 4 часа. Сколько км пройдет теплоход по озеру за 2 часа с той же собственной скоростью?

Answer 1

Пусть х км/ч - скорость течениятогда время в пути 56-10=46 часов теплоход находился в путих+23 км/ч - скорость по течению23-х - скорость против течения504/(23+х) + 504/(23-х)=46504*(23-х)+504*(23+х)=46*(23-х)*(23+х)2*504*23=46*(529-х²)504=529-х²25=х²х=5 км/ч

Answer 2

Problem Analysis

We are given that a boat traveled 93 km downstream in 3 hours and 100 km upstream in 4 hours. We need to find out how far the boat will travel on a lake in 2 hours at the same speed.

Solution

To solve this problem, we can use the concept of relative speed. The speed of the boat with respect to the water is constant, so we can assume it to be 'x' km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current.

Let's denote the speed of the river current as 'y' km/h.

Given that the boat traveled 93 km downstream in 3 hours, we can set up the equation: 93 = (x + y) * 3

Given that the boat traveled 100 km upstream in 4 hours, we can set up the equation: 100 = (x - y) * 4

We can solve these two equations to find the values of 'x' and 'y'.

Let's solve the equations:

From the first equation, we have: (x + y) = 93/3 x + y = 31

From the second equation, we have: (x - y) = 100/4 x - y = 25

Now, we can solve these two equations simultaneously to find the values of 'x' and 'y'.

Adding the two equations, we get: 2x = 31 + 25 2x = 56 x = 56/2 x = 28

Substituting the value of 'x' in one of the equations, we get: 28 + y = 31 y = 31 - 28 y = 3

So, the speed of the boat is 28 km/h and the speed of the river current is 3 km/h.

Now, we can calculate the distance the boat will travel on the lake in 2 hours at the same speed.

The distance traveled is given by the formula: distance = speed * time.

Substituting the values, we get: distance = 28 km/h * 2 hours distance = 56 km

Therefore, the boat will travel 56 km on the lake in 2 hours at the same speed.

Answer

The boat will travel 56 km on the lake in 2 hours at the same speed.