To analyze and understand how many days it takes to complete the task of making these shirts, we must know the total number of these shirts and the actual number of them produced every day. Knowing that the original plan was to produce 400 pieces a day and complete them in 60 days, we can find out the total number of these shirts; Knowing that the number of pieces actually produced every day is 65438+ 0.5 times of the original planned number, we can find out the number of pieces actually produced every day.
The actual number of days to complete these shirt-making tasks is:
40060(400 1.5)
=24000600
=40 days
It can also be considered that the total number of shirts to be produced is certain, so the number of days required to complete the task of making these shirts is inversely proportional to the number of shirts produced every day. It can be concluded that the number of days to actually complete the task of making these shirts is 1.5 times, which is exactly 60 days, so it is concluded that the number of days actually needed to make these shirts is:
60 1.5=40 (days)
A: It actually took 40 days to complete the task of making these shirts.
Example 2: Dongfeng Machinery Factory originally planned to produce 240 parts per day, which was completed in 18 days. It was actually finished three days ahead of schedule. How many more parts are actually produced every day than originally planned?
Analysis and solutions require how many more parts are actually produced every day than originally planned. First, find out the number of parts actually produced every day, and then subtract the number of parts planned to be produced every day:
240 18( 18-3)-240
=4320 15-240
=288-240
=48 (pieces)
You can also think that the total number of parts actually completed and planned is the same. According to the meaning of inverse proportion, the number of parts produced every day is inversely proportional to the number of days required to complete the production of these parts. Therefore, the ratio of the number of days originally planned to complete the task to the number of days actually completed the task is 18: (18-3), that is, 6: 5, that is, the ratio of the number of parts actually produced every day to the number of parts originally planned to produce every day. Of course, the actual number of parts produced every day is 6/5 of the original planned number of parts produced every day. So find out the number of parts actually produced every day than originally planned:
=48 (pieces)
You can also think of it this way: the total number of parts produced is 240 18=4320 (pieces); This number is decomposed into prime factors, and then the decomposed prime factors are appropriately grouped to represent the product of the original planned daily production number and the number of completed days and the product of the actual daily production number and the actual number of completed days respectively.
4320=25×33×5
= (24× 35) (232) ... The quantity and completion of the original planned daily output.
Tiande products
= (25× 32 )× (35) ... Actual daily output and days of completion.
product
Then find out how much the actual daily output exceeds the original plan:
25×32-24×35
=288-240
=48 (pieces)
A: Actually, 48 more units are produced every day than originally planned.
There are many more. Go and see for yourself.