Question

Помогите решить велосипедист проехал 60 км из пункта А в пункт В.На обратном пути он первый час проехал с прежней скоростью после чего сделал остановку на 20 мин.Начав движение снова , он увеличил скорость на 4 км/ч и поэтому потратил на путь из В в А столько же времени, сколько и на путь из А в В. Определите скорость велосипедиста на пути из А в В

Answer 1

Пусть х км/ч - скорость из А в B, х+4 - скорость на обратном пути после остановки.
$\frac{60}{x} = 1+1/3+ \frac{60-x}{x+4}$
$\frac{60-x}{x+4}$-$\frac{60}{x}$=-4/3
3x(60-x)-180(х+4)=-4х(х+4)
180х-3х²-180х-720+4х²+16х=0
х²+16х-720=0
По теореме Виета х₁=-36; х₂=20
Ответ. 20 км/ч

Answer 2

Problem Analysis

We are given that a cyclist traveled 60 km from point A to point B. On the return trip, the cyclist initially traveled at the same speed as before, then stopped for 20 minutes, and finally increased their speed by 4 km/h. The total time taken for the return trip is the same as the time taken for the initial trip. We need to determine the cyclist's speed from point A to point B.

Solution

Let's assume the cyclist's speed from point A to point B is x km/h.

On the initial trip from A to B, the cyclist traveled a distance of 60 km at a speed of x km/h. Therefore, the time taken for the initial trip is given by:

Time taken for initial trip = Distance / Speed = 60 km / x km/h = 60/x hours

On the return trip from B to A, the cyclist initially traveled at the same speed of x km/h for 1 hour. Then, the cyclist stopped for 20 minutes, which is equivalent to 20/60 = 1/3 hour. After the stop, the cyclist increased their speed by 4 km/h, so the speed for the return trip is (x + 4) km/h. The time taken for the return trip is the same as the time taken for the initial trip, so we can set up the following equation:

Time taken for return trip = Time taken for initial trip

Using the information above, we can write the equation:

1 hour + 1/3 hour + (Distance / (x + 4)) hours = 60/x hours

Simplifying the equation:

1 + 1/3 + (60 / (x + 4)) = 60/x

Multiplying through by 3x(x + 4) to eliminate the fractions:

3x(x + 4) + x(x + 4) + 180 = 60(x + 4)

Simplifying further:

3x^2 + 12x + x^2 + 4x + 180 = 60x + 240

Combining like terms:

4x^2 + 16x + 180 = 60x + 240

Rearranging the equation:

4x^2 - 44x + 60 = 0

Dividing through by 4:

x^2 - 11x + 15 = 0

Factoring the quadratic equation:

(x - 3)(x - 5) = 0

Setting each factor equal to zero:

x - 3 = 0 or x - 5 = 0

Solving for x:

x = 3 or x = 5

The cyclist's speed from point A to point B can be either 3 km/h or 5 km/h.

Answer

The cyclist's speed from point A to point B can be either 3 km/h or 5 km/h.