Question

Из пункта А в пункт В вышел поезд со скоростью 72 км/ч. Через 45 минут вышел поезд из В в А со скоростью 75 км/ч. Расстояние между А и В равно 348 км. На каком расстоянии от В поезда встретятся?

Answer 1

45мин=3/4ч

1)72*3:4=54(км)-пройдет от пункта А поезд за 45мин до выхода поезда из пункта В

2)348-54=294(км)-осталось пройти поещдам до встречи

3)72+75=147(кмЧ)-общая скорость

4)294:147=2(ч)-через 2ч поезда встретятся

5)2*75=150(км)-от пункта В произойдет встреча

Answer 2

Problem Analysis

We are given that a train leaves point A and travels towards point B at a speed of 72 km/h. After 45 minutes, another train leaves point B and travels towards point A at a speed of 75 km/h. The distance between points A and B is 348 km. We need to determine at what distance from point B the two trains will meet.

Solution

To solve this problem, we can use the formula:

Distance = Speed x Time

Let's assume that the two trains meet at a distance x from point B.

The first train travels for 45 minutes, which is equal to 45/60 = 0.75 hours. Therefore, the distance traveled by the first train is:

Distance1 = Speed1 x Time1 = 72 km/h x 0.75 h

The second train travels for the remaining time it takes for the two trains to meet, which is 45 minutes less than the total time it takes for the second train to travel from point B to point A. Let's denote this time as t.

The total time it takes for the second train to travel from point B to point A is given by:

Total Time = Time1 + t

The distance traveled by the second train is:

Distance2 = Speed2 x t = 75 km/h x t

Since the total distance traveled by both trains is equal to the distance between points A and B, we can write the equation:

Distance1 + Distance2 = 348 km

Substituting the expressions for Distance1 and Distance2, we get:

(72 km/h x 0.75 h) + (75 km/h x t) = 348 km

Simplifying the equation, we have:

54 km + 75t = 348 km

Solving for t, we find:

t = (348 km - 54 km) / 75 km/h

Now that we have the value of t, we can substitute it back into the equation for Distance2 to find the distance traveled by the second train:

Distance2 = 75 km/h x t

Finally, we can calculate the distance from point B where the two trains will meet by subtracting the distance traveled by the second train from the total distance between points A and B:

Distance from B = 348 km - Distance2

Let's calculate the values:

Distance1 = 72 km/h x 0.75 h = 54 km

t = (348 km - 54 km) / 75 km/h

Distance2 = 75 km/h x t

Distance from B = 348 km - Distance2

Calculation

Distance1 = 54 km

t = (348 km - 54 km) / 75 km/h

Distance2 = 75 km/h x t

Distance from B = 348 km - Distance2

Using the given values, we can calculate the solution.

Distance1 = 54 km

t = (348 km - 54 km) / 75 km/h = 294 km / 75 km/h = 3.92 hours

Distance2 = 75 km/h x 3.92 h = 294 km

Distance from B = 348 km - 294 km = 54 km

Therefore, the two trains will meet at a distance of 54 km from point B.

Answer

The two trains will meet at a distance of 54 km from point B.