Question

Из пункта а в пункт б велосипедиста проехал по одной дороге 27км, а обратно возвращался по другой дороге, которая была короче первой на 7 км. Хотя на обратном пути велосипедиста уменьшил скорость на 3 км/чч а на обратный путь экстраординарного на 10 минут меньше, чем на путь из А в Б. С какой скоростью ехал велосипедиста из А в Б

Answer 1

Х км/ч - скорость из А в В
х-3 км/ч - скорость на обратном пути
27/х ч - время в пути из А в В
(27-7)/(х-3) ч - время на обратном пути, на 10 мин меньше
10 мин=1/6 ч

27/х-(27-7)/(х-3)=1/6
27*6(х-3) - 20*6х=х(х-3)
162х-486-120х=х²-3х
х²  - 45х+486=0
D=45²-4*486=81=+-9²
х1=(45+9)/2=27 - не подходит, т.к. слишком большая скорость для вело
х2=(45-9)/2=18(км/ч) - скорость велосипедиста из А в В

Answer 2

Problem Analysis

A cyclist traveled from point A to point B along one road, covering a distance of 27 km. On the return journey, the cyclist took a different road that was 7 km shorter than the first road. The cyclist reduced their speed by 3 km/h on the return journey and took 10 minutes less than the time taken for the journey from A to B. We need to determine the speed at which the cyclist traveled from A to B.

Solution

Let's break down the information given in the problem: - Distance from A to B: 27 km - Distance from B to A (return journey): 27 km - 7 km = 20 km - Speed reduction on the return journey: 3 km/h - Time reduction on the return journey: 10 minutes

To find the speed at which the cyclist traveled from A to B, we can set up the following equation:

Speed from A to B = Distance from A to B / Time from A to B

Let's calculate the time taken for the journey from A to B and the time taken for the return journey.

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

Time from A to B = Distance from A to B / Speed from A to B

The time taken for the return journey can be calculated using the formula:

Time for return journey = Distance from B to A / Speed from B to A

We know that the speed from B to A is the speed from A to B minus the speed reduction on the return journey:

Speed from B to A = Speed from A to B - Speed reduction

We also know that the time for the return journey is 10 minutes less than the time for the journey from A to B:

Time for return journey = Time from A to B - 10 minutes

Now we can substitute the values into the equations and solve for the speed from A to B.

Calculation

Let's calculate the speed at which the cyclist traveled from A to B.

Distance from A to B = 27 km Distance from B to A = 20 km (27 km - 7 km) Speed reduction on the return journey = 3 km/h Time reduction on the return journey = 10 minutes

Using the formula for time:

Time from A to B = Distance from A to B / Speed from A to B

Time for return journey = Distance from B to A / Speed from B to A

Speed from B to A = Speed from A to B - Speed reduction

Time for return journey = Time from A to B - 10 minutes

Let's substitute the values into the equations and solve for the speed from A to B.

Time from A to B = 27 km / Speed from A to B

Time for return journey = 20 km / (Speed from A to B - 3 km/h)

20 km / (Speed from A to B - 3 km/h) = 27 km / Speed from A to B - 10 minutes

Converting 10 minutes to hours:

10 minutes = 10/60 hours = 1/6 hours

20 km / (Speed from A to B - 3 km/h) = 27 km / Speed from A to B - 1/6 hours

To simplify the equation, let's multiply both sides by the denominators:

20 km * Speed from A to B = 27 km * (Speed from A to B - 3 km/h) - (1/6 hours) * (Speed from A to B - 3 km/h)

20 km * Speed from A to B = 27 km * Speed from A to B - 81 km^2/h - (1/6 hours) * Speed from A to B + (1/6 hours) * 3 km/h

Multiplying through by 6 to eliminate the fraction:

120 km * Speed from A to B = 162 km * Speed from A to B - 486 km^2/h - Speed from A to B + 3 km/h

Combining like terms:

120 km * Speed from A to B - 162 km * Speed from A to B + Speed from A to B = 3 km/h - 486 km^2/h

-42 km * Speed from A to B = -483 km^2/h

Dividing both sides by -42 km:

Speed from A to B = -483 km^2/h / -42 km

Speed from A to B = 11.5 km/h

Answer

The cyclist traveled from point A to point B at a speed of 11.5 km/h.

Explanation

The speed at which the cyclist traveled from A to B was calculated using the given information about the distances, speed reduction, and time reduction on the return journey. By setting up equations and solving for the unknown speed, we determined that the cyclist traveled at a speed of 11.5 km/h from A to B.