Question

В трёх составах 120 товарных вагонов. В первом и втором составах вместе 77 вагонов, во втором и третьем-70 вагонов. Сколько вагонов в каждом составе? Сделать чертёж и решить задачу. На видеокассету, рассчитанную на 210 мин. записали два фильма: первый длится 1ч 38мин ,второй- 1ч 27мин. Можно ли на эту кассету записать ещё фильм , который длится 23 мин?

Answer 1

№1.

| ____?____|____?___ |____?____|

|_________77_______|

                 |_________70________|

|_____________120____________|

 

1) 120-77=43 (в.) - в 3-м составе

2) 120-70=50 (в.) - в 1-м составе

3) 77-50=27 (в.) - во 2-м составе

Ответ: в первом составе 50 вагонов, во втором - 27 вагонов, а в третьем - 43 вагона.

 

№2.

1 ч. 38 мин.=98 мин.

1 ч. 27 мин.=87 мин.

1) 98+87=185 (мин.) - уже записали

2) 210-185=25 (мин.) - осталось

25 мин.>23 мин.

Ответ: да, можно записать на эту кассету фильм, который длится 23 минуты.

Answer 2

Problem 1: Number of Wagons in Each Composition

To solve this problem, we need to determine the number of wagons in each composition based on the given information.

Let's break down the information provided:

- In the first and second compositions together, there are 77 wagons. - In the second and third compositions together, there are 70 wagons. - The total number of wagons in all three compositions is 120.

To find the number of wagons in each composition, we can set up a system of equations.

Let's assume: - The number of wagons in the first composition is x. - The number of wagons in the second composition is y. - The number of wagons in the third composition is z.

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

Equation 1: x + y = 77 (from the first and second compositions together) Equation 2: y + z = 70 (from the second and third compositions together) Equation 3: x + y + z = 120 (total number of wagons in all three compositions)

To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method:

Adding Equation 1 and Equation 2, we get: (x + y) + (y + z) = 77 + 70 x + 2y + z = 147 (Equation 4)

Subtracting Equation 3 from Equation 4, we get: (x + 2y + z) - (x + y + z) = 147 - 120 x + 2y + z - x - y - z = 27 y = 27

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:

x + y = 77 x + 27 = 77 x = 77 - 27 x = 50

Similarly, we can substitute the value of y into Equation 2 to find the value of z:

y + z = 70 27 + z = 70 z = 70 - 27 z = 43

Therefore, the number of wagons in each composition is as follows: - First composition: 50 wagons - Second composition: 27 wagons - Third composition: 43 wagons

Problem 2: Recording Films on a Videocassette

To determine if it is possible to record an additional film on a videocassette that is already recorded with two films, we need to calculate the total duration of the two films and compare it with the remaining duration on the videocassette.

Let's calculate the total duration of the two films:

- The first film lasts 1 hour and 38 minutes, which is equivalent to 98 minutes. - The second film lasts 1 hour and 27 minutes, which is equivalent to 87 minutes.

The total duration of the two films is 98 minutes + 87 minutes = 185 minutes.

The videocassette is initially recorded for 210 minutes.

To determine if there is enough remaining duration on the videocassette to record an additional film that lasts 23 minutes, we subtract the total duration of the two films from the initial duration of the videocassette:

210 minutes - 185 minutes = 25 minutes

Since there are 25 minutes remaining on the videocassette after recording the two films, it is indeed possible to record an additional film that lasts 23 minutes.

Therefore, it is possible to record another film that lasts 23 minutes on the videocassette.

I hope this helps! Let me know if you have any further questions.