(2005? Taizhou) There is a water dispenser in the classroom (pictured). There are two water pipes on the drinking fountain. During the break, the students take turns to use cups to pick up water from the water dispenser. Assuming that the water does not overflow in the process of receiving water, then each student receives the same amount of water. When two water pipes are opened at the same time, their flow rates are the same. When draining water, first open a pipe, then open a second pipe, and the valve is always open during draining water.

(1) Find the functional relationship between water storage y (liter) and water discharge time x (minute) (x≥2);

(2) If after the first water pipe is turned on, it happens that four students finish drinking water within 2 minutes, how many minutes will it take for the first 22 students to finish drinking water?

(3) According to (2), how many students in the class can finish the water in time within 10 minutes between classes?

Test center: the application of linear function.

Special topic: reading type; Chart type.

Analysis: (1) It is known from the image that the straight line passes through points (2 17) and (12,8), and it can be solved by substituting it into the equation;

(2)(3) Small questions can be answered according to the functional relationship between water storage capacity and discharge time.

Solution: Solution: (1) Assume that the analytical formula of water storage y and drainage time x is y=kx+b,

Substitute (2, 17) and (12,8) into y=kx+b,

Get 17=2k+b8= 12k+b,

The solution is k=-9 10, and b=945.

Therefore, y =-910x+945 (2 ≤ x ≤1889);

(2) According to the picture, the water consumption of each student is 0.25 liters.

Then the first (22-4) students need to receive 0.25× 18=4.5 liters of water.

Water storage y =18-1-4.5 =12.5l,

∫ When two drainage pipes are opened at the same time, the flow rate is: 17-8 12-2=0.9.

∴4.50.9=5,

∴ It takes 5+2=7 minutes for the first 22 students to receive water * * *;

(3) When x= 10, according to formula (2), four students are picked up two minutes before receiving water, and the water storage capacity of the water dispenser is maintained for eight minutes.

The water flow of the drinking machine in these 8 minutes is 8×0.9=7.2 liters.

So 7.20.25=28.8,

Then 28.8+4=32.8,

Then the number of people who can finish drinking water in time during recess 10 minutes is 4+28.8 = 32.8 ≈ 32.

So at most 32 people drink the water in time within 10 minutes between classes.

Comments: This topic mainly examines how to use the undetermined coefficient method to find the linear function relationship, and will use the linear function to study practical problems, with the ability to read maps in rectangular coordinate system.