Mathematical problems of ticket checking at ticket gate

Prompt: Set the ticket gate of 1 ticket per minute, and the number of new passengers per minute is 1:

(3× 40-4× 25) ÷ (40-25) = 4/3 (number of copies)

Find the original number of passengers: 3× 40-40× 4/3 = 200/3 (copies) or 4× 25-25× 4/3 = 200/3 (copies).

(3-4/3) × 40 = 200/3 4/3 indicates the ticket gates needed by new passengers, and (3-4/3) indicates that the remaining ticket gates will check the original passengers for 40 minutes.

The time required to open eight ticket gates is: 200/3 ÷ (8-4/3) = 10 (minutes) (8-4/3), which indicates the number of ticket gates for the remaining passengers, that is, the number of tickets checked per minute.

If you don't quite understand, I'll give you a solution and another way of thinking, provided that you learn to solve equations simply.

3 X 40-4 X 25 = 120- 100 = 20

(40-25)/20=3/4 This means that 1 window can check the tickets of 3/4 X tourists every minute, that is, the work efficiency. .

(3X40X0.75)-40=50, which means there are 50(X) people waiting there.

Therefore, the working efficiency of 8 windows, each with 3/4X, needs to complete the existing 50X+XT people.

At this point, we can calculate

(40+50)/ 3/0.75 = 40 (minutes) means that three windows have solved everyone in 40 minutes.

(25+50)/ 4/0.75 = 25 (minutes) means four windows for 25 minutes, which is consistent with the previous question.

Then, let time be t.

(T+50)/ 8 / 0.75 =T

Solve this unary equation and get

T+50 = 6 tons

T= 10 (minutes)

If you have studied equations, you can understand the topic like this.

There is a station where Z people line up. X people will come every minute in the future. If three people are allowed to check in (those who have checked in first will continue to queue up until no one comes and the ticket is checked), all the people who want to take the bus will be checked in 40 minutes. If four people check in, it will take 25 minutes. Q: How many minutes does it take for eight people to check in?

Let x be the number of people coming in every minute.

Y is the working efficiency of the ticket checking window.

There are Z people in line.

40*X+Z=3*40*Y=== 1

25*X+Z=4*25*Y===2

1 minus 2

15X=20Y

Y=3/4 X========3

Substitute 1 to get

Z+40X= 120*3/4 X

= = = =》Z = 50X = = = = = = = 4

It takes t minutes to arrange another 8 people.