Question

Расстояние от пункта А до пункта б велосипед проехал за 3 часа, на обратном пути он увеличил скорость на 2 км/ч и поэтому затратил на обратный путь на 30 мин меньше. С какой скоростью ехал велосипедист из пункта А в пунк Б? ПОМОГИТЕ ПОЖААААЛУЙСТА, ОЧЕНЬ СРОЧНО НУЖНО:*

Answer 1

Х-скорость
3х=2.5(х+2)
3х=2,5х+5
0,5х=5
х=10км/ч-скорость из а в б

Answer 2

Problem Analysis

We are given that a cyclist traveled from point A to point B in 3 hours. On the return trip, the cyclist increased their speed by 2 km/h and spent 30 minutes less. We need to find the speed at which the cyclist traveled from point A to point B.

Solution

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

On the return trip, the cyclist increased their speed by 2 km/h, so the speed from point B to point A is (x + 2) km/h.

We know that the time taken for the return trip is 30 minutes less than the time taken for the forward trip. Since 30 minutes is equal to 0.5 hours, we can write the equation:

Time taken for the forward trip = Time taken for the return trip + 0.5 hours

Using the formula time = distance / speed, we can write the equation:

Distance from A to B / x = Distance from B to A / (x + 2) + 0.5

To solve for x, we need to find the distances from A to B and from B to A.

Finding the Distances

Unfortunately, the given information does not provide the distances directly. We need to find another way to determine the distances.

Let's assume the distance from point A to point B is d km.

Using the formula distance = speed * time, we can write the equations:

d = x * 3 (forward trip)

d = (x + 2) * (3 - 0.5) (return trip)

Simplifying the equations:

d = 3x

d = 2.5x + 3

Now we have a system of equations that we can solve to find the value of x.

Solving the System of Equations

Substituting the value of d from the first equation into the second equation:

3x = 2.5x + 3

Simplifying the equation:

0.5x = 3

x = 6

Therefore, the speed at which the cyclist traveled from point A to point B is 6 km/h.

Answer

The cyclist traveled from point A to point B at a speed of 6 km/h.

Verification

Let's verify our answer by substituting the value of x into the equations we derived earlier.

Using the equation d = 3x:

d = 3 * 6 = 18 km

Using the equation d = 2.5x + 3:

d = 2.5 * 6 + 3 = 15 + 3 = 18 km

The distances from A to B and from B to A are both 18 km, which confirms our answer.

Conclusion

The cyclist traveled from point A to point B at a speed of 6 km/h. The distances from A to B and from B to A are both 18 km.