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 систему 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

We have two pedestrians walking towards each other. One is walking from point A to point B, while the other is walking from point B to point A. They start at the same time, and when the first pedestrian has walked half the distance, the second pedestrian still has 1.5 hours left to walk. When the second pedestrian has walked half the distance, the first pedestrian still has 45 minutes left to walk. We need to determine how much earlier the first pedestrian will finish their journey compared to the second pedestrian.

Solution

Let's assume that the total distance between points A and B is d.

When the first pedestrian has walked half the distance, they have covered d/2. At this point, the second pedestrian still has 1.5 hours left to walk. Let's denote the speed of the first pedestrian as v1 and the speed of the second pedestrian as v2.

Using the formula distance = speed × time, we can write the following equation for the first pedestrian: d/2 = v1 × t1, where t1 is the time taken by the first pedestrian to cover half the distance.

Similarly, for the second pedestrian, when they have walked half the distance, they have covered d/2. At this point, the first pedestrian still has 45 minutes left to walk. We can write the following equation for the second pedestrian: d/2 = v2 × t2, where t2 is the time taken by the second pedestrian to cover half the distance.

We can solve these two equations to find the values of t1 and t2. Then, we can calculate the total time taken by each pedestrian to complete their journey.

Finally, we can subtract the time taken by the second pedestrian from the time taken by the first pedestrian to find out how much earlier the first pedestrian finishes their journey compared to the second pedestrian.

Calculation

Let's solve the equations to find the values of t1 and t2.

From the first equation, we have: d/2 = v1 × t1 [Equation 1]

From the second equation, we have: d/2 = v2 × t2 [Equation 2]

We can rearrange Equation 1 to solve for t1: t1 = (d/2) / v1

Similarly, we can rearrange Equation 2 to solve for t2: t2 = (d/2) / v2

Now, let's substitute the given values into the equations: - When the first pedestrian has walked half the distance, the second pedestrian has 1.5 hours left to walk. So, t1 = 1.5 hours. - When the second pedestrian has walked half the distance, the first pedestrian has 45 minutes left to walk. So, t2 = 45 minutes.

Now, we can calculate the total time taken by each pedestrian to complete their journey: - Total time taken by the first pedestrian: 2 × t1 - Total time taken by the second pedestrian: 2 × t2

Finally, we can subtract the time taken by the second pedestrian from the time taken by the first pedestrian to find out how much earlier the first pedestrian finishes their journey compared to the second pedestrian.

Let's perform the calculations.