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Solving four math problems "Hua Luogeng Jinbei" is an important process in the fifth grade of primary school. You better tell me why.
1. Insert a stick into the water. The stick was 60 centimeters wet. Then turn the stick upside down and insert it into the water. At this point, the wet part of the stick is 20 cm shorter than its half. How long is this stick?

Still 60cm, both sides are wet, that is, the wet part is 120cm, so the length of the stick is (120+20)*2=280cm.

When an object falls from the sky, it is known that the distance it falls in the first second is 4.9 meters, and the distance it falls in the next second is 9.8 meters more than that in the previous second. After 20 seconds, the object landed. How far was the object from the ground before it fell?

The first second: 4.9, the second: 4.9+9.8, the third: 4.9+9.8 * 2 ... the nth second: 4.9+9.8*(n- 1).

Ground distance = 4.9 * 20+9.8 * (1+2+3+...+19) = 4.9 * 20+9.8 * (20 * 9+10) = 4.9 * 20+9.

= 9.8 * 10+9.8 * 190 = 9.8 * 200 = 1960m

Party A and Party B ride bicycles from place A to place B at the same time. In the first three hours, Party A delayed repairing the car for 1 hour. As a result, Party B was 6 kilometers ahead of Party A ... After another three hours, A was 3 kilometers ahead of B. How many meters did A and B ride every hour?

According to the meaning of the question, both parties drive at the same time. (1) Party B drives for 6 hours, which is 3 kilometers less than Party A's 5 hours.

(2)B travels for 3 hours, 6 kilometers more than A travels for 2 hours. That is to say, if B drives for 6 hours, it will drive more than A for 4 hours 12 km (2 for both times).

According to (1)(2), the driving distance of A in one hour is 12+3 = 15km.

Then the hourly driving distance in Otsuichi is (15 * 4+12)/6 =12km.

4. The TV factory has completed the task of assembling a batch of TV sets, and now 635 sets have been installed. If two more units are assembled every hour, it will take 40 hours to complete, but five units will be installed in the last hour; If you still assemble according to the original work efficiency, you need to work for 3 more hours. How many TV sets are there in this batch?

It takes 43 hours at the original speed,

It took 40 hours after the acceleration, but five units were installed in the last hour, so two units were installed in 39 hours and five units were installed in the last hour.

Compared with the original speed, the extra 4 hours at the original speed accelerated the workload by 2 units per hour and 5 units in the last hour, as shown in the following figure:

1~39 hours original original original speed 40 hours original speed 4 1~42 hours original speed 43 hours original speed x platform (x

Acceleration 1~39 hours original speed +2 40th hour 5

So the number of units dried at the original speed of 3 hours = 5+2 * 39-x = 83-x.

Since the number of units can only be integers, x = 2, 5, 8, 1 1, 14,17,20 (the maximum value is 20, because at 23: 00, the output of the last hour will be greater than the stable output, which is impossible).

The original production units per hour are 27, 26, 25, 24, 23, 22, 2 1.

Since 635 units have been installed, the original number of units produced per hour is 25 (because everything else is not an integer, such as 635/27=23.5 units, it is obviously impossible to produce 23.5 units per hour).

The number of these TV sets is 25*43+635= 17 10.