Question

Из пунктов A и B, расстояние между которыми 35 км, навстречу друг другу вышли два пешехода. Если пешеход, вышедший из пункта А, выйдет на 3 ч раньше второго пешехода, то они встретятся через 2,5 ч после выхода пешехода из пункта B. Если же пешеход, вышедший из пункта B, выйдет на 1 ч раньше первого, то они встретятся через 5 ч после выхода пешехода из пункта А. Определите скорости обоих пешеходов.

Answer 1

Ответ:

Объяснение:

$\begin{cases}(3+2.5)v_A+2.5v_B=35\\5v_A+(1+5)v_B=35\end{cases}\begin{cases}11v_A+5v_B=70\\10v_A+12v_B=70\end{cases}\\\\v_A=7v_B\\77v_B+5v_B=70\\v_B=\dfrac{70}{82}=\dfrac{35}{41}\\v_A=7\cdot\dfrac{35}{41}=\dfrac{245}{41}$

Answer 2

Problem Analysis

We have two pedestrians who start walking towards each other from points A and B, which are 35 km apart. The first pedestrian, who starts from point A, arrives 2.5 hours after the second pedestrian, who starts from point B, if the first pedestrian starts 3 hours earlier. On the other hand, if the second pedestrian starts 1 hour earlier, they will meet 5 hours after the first pedestrian starts from point A. We need to determine the speeds of both pedestrians.

Solution

Let's assume the speed of the first pedestrian (starting from point A) is v1 km/h, and the speed of the second pedestrian (starting from point B) is v2 km/h.

To find the speeds, we can use the formula: speed = distance / time.

From the given information, we can derive the following equations:

1. When the first pedestrian starts 3 hours earlier: - Distance covered by the first pedestrian: 35 km - Time taken by the first pedestrian: t1 hours - Time taken by the second pedestrian: t1 + 2.5 hours - Using the formula, we have: v1 = 35 / t1 and v2 = 35 / (t1 + 2.5)

2. When the second pedestrian starts 1 hour earlier: - Distance covered by the second pedestrian: 35 km - Time taken by the first pedestrian: t2 + 5 hours - Time taken by the second pedestrian: t2 hours - Using the formula, we have: v1 = 35 / (t2 + 5) and v2 = 35 / t2

We now have a system of equations that we can solve to find the values of v1 and v2.

Solving the Equations

Let's solve the system of equations using substitution:

From the first set of equations: - v1 = 35 / t1 - v2 = 35 / (t1 + 2.5)

From the second set of equations: - v1 = 35 / (t2 + 5) - v2 = 35 / t2

We can equate v1 from both sets of equations: - 35 / t1 = 35 / (t2 + 5)

Simplifying the equation: - t1 = t2 + 5

Substituting this value of t1 into the first set of equations: - v1 = 35 / (t2 + 5) - v2 = 35 / (t2 + 2.5)

Now we have two equations with two variables. We can solve this system of equations to find the values of v1 and v2.

Let's solve the equations:

1. v1 = 35 / (t2 + 5) 2. v2 = 35 / (t2 + 2.5)

Substituting the value of v1 from equation 1 into equation 2: - 35 / (t2 + 5) = 35 / (t2 + 2.5)

Cross-multiplying: - 35(t2 + 2.5) = 35(t2 + 5)

Expanding and simplifying: - 35t2 + 87.5 = 35t2 + 175

Simplifying further: - 87.5 = 175

This equation is not possible to solve because it leads to a contradiction. Therefore, there is no solution to this problem.

Conclusion

Based on the given information, there is no possible solution to determine the speeds of both pedestrians. The equations derived from the problem lead to a contradiction, indicating that the problem is not solvable with the given information.