Question

Велосипедист выехал с постоянной скоростью из города А в город В, расстояние между которыми равно 78 км. На следующий день он отправился обратно со скоростью на 7 км/ч больше прежней. По дороге он сделал остановку на 7 часов. В результате он затратил на обратный путь столько же времени, сколько на путь из А в В. Найдите скорость велосипедиста на пути из А в В. помогите пожалуйста.

Answer 1

х-скорость

t-время

 

х*t=78

(х+7)*(t-7)=78

х=78/t

(78/t+7)*(t-7)=78

78+7t-546/t-49=78

7t-546t=49

(7t^2-546)/t=49

(7*(t^2-78))/t=49

(t^2-78)/t=7

t^2-78=7t

t^2-7t-78=0

Д=361 корень из Д=19

 

t1=(7-19)^2=-6  не подходит

t2=(7+19):2=13 часов ехал велосипедист в первый день

13-7=6 часов ехал велосипедист во второй день

 

х1=78:13=6км/ч скорость велосипедиста из А в В

х2=78:(6+7)=13км/ч скорость велосипедиста из В в А

 

 

Answer 2

Problem Analysis

We are given that a cyclist travels from city A to city B at a constant speed. The distance between the two cities is 78 km. On the next day, the cyclist returns from city B to city A at a speed that is 7 km/h faster than the previous day. The cyclist makes a 7-hour stop on the way back. We need to find the speed of the cyclist on the way from city A to city B.

Solution

Let's assume the speed of the cyclist on the way from city A to city B is x km/h.

On the way from city B to city A, the cyclist's speed is x + 7 km/h.

We are given that the time taken for the return journey is the same as the time taken for the journey from city A to city B.

To find the speed of the cyclist on the way from city A to city B, we can set up the following equation:

Time taken for the journey from A to B = Time taken for the return journey

The time taken for the journey from A to B can be calculated using the formula:

Time = Distance / Speed

The distance from A to B is 78 km, and the speed is x km/h. Therefore, the time taken for the journey from A to B is:

Time taken for the journey from A to B = 78 / x

The time taken for the return journey can be calculated as follows:

Time taken for the return journey = Time taken for the journey from B to A + Stoppage time

The time taken for the journey from B to A can be calculated using the formula:

Time = Distance / Speed

The distance from B to A is also 78 km, and the speed is (x + 7) km/h. Therefore, the time taken for the journey from B to A is:

Time taken for the journey from B to A = 78 / (x + 7)

Adding the stoppage time of 7 hours, we get:

Time taken for the return journey = 78 / (x + 7) + 7

Now, we can set up the equation:

Time taken for the journey from A to B = Time taken for the return journey

78 / x = 78 / (x + 7) + 7

To solve this equation, we can cross-multiply and simplify:

78(x + 7) = 78x + 7(78)

Simplifying further:

78x + 546 = 78x + 546

We can see that the equation simplifies to 546 = 546. This means that the equation is true for all values of x.

Therefore, the speed of the cyclist on the way from city A to city B can be any value.

In conclusion, the speed of the cyclist on the way from city A to city B can be any value.