Question

Велосипедист проехал путь от А до В, равный 60 ем, с постоянной скоростью. На обратном пути он первый час ехал с прежней скоростью, после чего сделал остановку на 20 минут. 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

Х-скорость велосипедиста на пути из А в В
60/х -время,потраченное на путь из А в В

обратный путь
1 ч ехал со скоростью х км/ч,значит
х(км)-путь,которые проехал за 1 час

60-х  -осталось проехать
х+4 км/ч - скорость
(60-х)/(х+4) -время движения со скоростью х+4 км/ч

20 мин=1/3 ч-остановка

всего на обратный путь он потратил
1 + 1/3 +(60-х)/(х+4)

составим уравнение
1 1/3+(60-х)/(х+4)=60/х ==== умножим на 3х(х+4)

4х(х+4)+3х(60-х)=180(х+4)
4х²+16х+180х-3х²-180х-720=0
х²+16х-720=0 

D=16²+4*720=3 136
√D=56
x1=(-16-56)/2=-36  км/ч не подходит
x2=(-16+56)/2=20 (км/ч) -искомая скорость

Ответ:20 км/ч.

Answer 2

Problem Analysis

A cyclist travels from point A to point B, covering a distance of 60 km at a constant speed. On the return journey, the cyclist initially travels at the same speed for one hour, then takes a 20-minute break. After resuming the journey, the cyclist increases their speed by 4 km/h. The goal is to determine the cyclist's speed on the journey from point A to point B.

Solution

Let's break down the problem step by step:

1. The cyclist covers a distance of 60 km from point A to point B at a constant speed. Let's assume the speed is x km/h. 2. On the return journey, the cyclist initially travels at the same speed for one hour, covering a distance of x km. 3. After the first hour, the cyclist takes a 20-minute break. 4. After the break, the cyclist resumes the journey and increases their speed by 4 km/h. Let's assume the new speed is (x + 4) km/h. 5. The cyclist covers the same distance from point B to point A in the same amount of time as the journey from point A to point B.

To find the cyclist's speed on the journey from point A to point B, we can use the formula:

Speed = Distance / Time

Let's calculate the time taken for each part of the journey:

1. Time taken for the journey from point A to point B: 60 km / x km/h = 60/x hours 2. Time taken for the journey from point B to point A: 60 km / (x + 4) km/h = 60/(x + 4) hours

According to the problem, the time taken for both journeys is the same. Therefore, we can set up the following equation:

60/x = 60/(x + 4)

Now, let's solve this equation to find the value of x, which represents the cyclist's speed on the journey from point A to point B.

Calculation

To solve the equation 60/x = 60/(x + 4), we can cross-multiply:

60(x + 4) = 60x

Expanding the equation:

60x + 240 = 60x

Subtracting 60x from both sides:

240 = 0

This equation has no solution, which means there is no valid speed for the cyclist on the journey from point A to point B that satisfies the given conditions.

Conclusion

Based on the given information, it is not possible to determine the cyclist's speed on the journey from point A to point B.