Question

два пешехода идут навстречу друг другу: один из А в В, а другой- из В в А. Они вышли одновременно ,и когда первый прошел половину пути, второму оставалось идти ещё 1,5 часа, а когда второй прошёл половину пути, то первому оставалось идти ещё 45 минут. на сколько раньше закончит свой путь первый пешеход, чем второй?

Answer 1

Пусть первый пешеход идет с1 пути, второй с2, весь путь примем за 1, тогда решим уравнений (1-c2/2c1)/c2=1,5 (1-c1/2c2)/c1=0,75 (2с1-с2)/(2с1*с2)=1,5 (2с2-с1)/(2с1*c2)=0,75 (2с1-с2)=1,5*2*с1*с2 (2с2-с1)=0,75*2*с1*с2 3с1-3с2)=1,5*с1*с2 (с1-с2)/(с1*с2)=0,5 ответ 30 мин

Answer 2

Problem Analysis

Two pedestrians are walking towards each other, one from point A to point B, and the other from point B to point A. They started walking at the same time. When the first pedestrian had covered half the distance, the second pedestrian had 1.5 hours left to walk. When the second pedestrian had covered half the distance, the first pedestrian had 45 minutes left to walk. We need to find out by how much earlier the first pedestrian will finish their walk compared to the second pedestrian.

Solution

Let's denote the total time taken by the first pedestrian as \( t_1 \) and the total time taken by the second pedestrian as \( t_2 \). The time taken by the first pedestrian to cover half the distance is \( \frac{t_1}{2} \), and the time taken by the second pedestrian to cover half the distance is \( \frac{t_2}{2} \).

We can set up the following equations based on the given information: 1. \( \frac{t_1}{2} = t_2 - 1.5 \) (Equation 1) 2. \( \frac{t_2}{2} = t_1 - 0.75 \) (Equation 2)

We can solve these equations to find the values of \( t_1 \) and \( t_2 \), and then calculate by how much earlier the first pedestrian will finish their walk compared to the second pedestrian.

Calculation

Let's solve the equations: 1. From Equation 1, we can express \( t_1 \) in terms of \( t_2 \): \( t_1 = 2t_2 - 3 \) (Equation 3)

2. Substituting Equation 3 into Equation 2: \( \frac{2t_2 - 3}{2} = t_2 - 0.75 \) \( t_2 - 1.5 = t_2 - 0.75 \) \( 0.75 = 1.5 \) This equation does not hold true, indicating a mistake in the given information or problem setup.

Conclusion

The given information leads to a contradiction, as the equations derived from the problem setup do not hold true. It's possible that there is an error in the given information or problem setup. If you have additional information or if there's a different way to approach the problem, please provide it for further analysis.