Analysis: It is easy to know that 2, 3, 4, 5, 6 and 7 are correct. 10, 12, 14, 15 are also correct.
So the wrong ones are 8 and 9.
So the minimum value of this five-digit number is1/kloc-0 /×13x14x415x2 = 60060.
2. Party A and Party B set out from the two vertices A and C opposite to the square pool ABCD with the circumference of 1600 meters, and walked along the edge of the pool in the direction of A-B-C-D-A. The speed of Party A was 50 meters per minute, and the speed of Party B was 46 meters per minute, so that Party A and Party B walked on the same side for the first time. How many minutes did you walk on the same side for the first time?
Analysis: In order for two people to walk on the same side, the distance between A and B must be less than one side, and A must cross the vertex. It takes at least 400÷(50-46)= 100 minutes100 = 5000m, 5000 ÷ 400 = 65438 to catch up with B. At this point, A has traveled 50×100 = 5000m. So it takes 200÷50=4 minutes to walk, that is, 100+4= 104 minutes after departure, and they walk on the same side for the first time.
At this time, the distance between Party A and Party B is 400×2- 104×(50-46)=384 meters, and Party B still has 16 meters to walk the same side for the first time, so it takes 16÷46=8/23 minutes.
3. A bus line has 15 stops (including starting point and ending point). Among those who get on the bus at each stop, one will get off at each stop in the future. How many seats are there for each passenger on the bus?
Analysis: the first stop 14× 1= 14 people, and the second stop 13×2=26 people.
The third station 12×3=36 people, and the fourth station 1 1×4=44 people.
The fifth station 10×5=50 people and the sixth station 9×6=54 people.
The seventh station is 8×7=56 people, and the eighth station is 7×8=56 people.
The ninth station is 6×9=54 people, and the 10 station is 5× 10=50 people.
……
So we have to prepare 56 seats.
A boat went upstream, and someone on board threw the kettle under the bridge and it was washed away by the water. It was already 20 minutes when the boat turned around. Later, the kettle was caught 2 kilometers downstream of the bridge. So what is the speed of the river?
Analysis: When the ship turns back, the distance between the kettle and the ship is equivalent to: the ship goes against the current for 20 minutes+the kettle runs for 20 minutes (the water flows for 20 minutes) = the ship stays in still water for 20 minutes.
In time, the speed difference between the ship and the kettle is equivalent to the speed of the ship-the speed of the kettle (current speed) = the still water speed of the ship.
So the time to catch the kettle is 20 minutes. That is, the kettle took 20×2=40 minutes and was washed away for 2 kilometers.
So the speed of water flow is 2÷40/60=3 kilometers per hour.
5. Transport the telephone poles from the material yard on the highway to the roadside 500 meters away and bury them, and plant one at the roadside every 50 meters. It is also known that only three lines can be transported at a time, and 20 poles should be transported back to the site. How to make reasonable arrangements to minimize the total journey of transport trucks? What's the minimum?
Analysis: Total * * * needs to send 20÷3≈7 round trips. Send them far away first, three at a time, and you will walk less. The total stroke is calculated as follows:
According to the method of 19, 16, 13, 10, 7, 4, 1 50 meters each, return to10× 7× 2 =/kloc-0.
So the * * line is 500×14+50×140 =14000m.
6. Master Wang wants to process a batch of parts. If 12 parts are processed per hour, it will take less time than planned 1/9. If we process less 16 pieces per hour, it will take 3/5 hours more than before. How many parts are there in this batch?
Analysis: The working hours are less 1/9, which means the working efficiency is improved1÷ (1-1/9)-1=1/8.
It shows that the original plan is to process 12÷ 1/8=96 pieces per hour.
If less 16 pieces are processed per hour, the work efficiency will be the original (96- 16)÷96=5/6,
The time will increase by1÷÷÷5/6-1=1/5.
So the original planned working time is 3/5÷ 1/5=3 hours.
So this batch of parts is 96×3=288.
7. Party A and Party B each process a certain number of parts. If Party A processes 24 parts per hour and Party B processes 12 parts per hour, then after Party B completes the task, Party A has 22 parts left. If Party A processes 12 pieces per hour and Party B processes 24 pieces per hour, then Party B will have 130 pieces left after completing the task. How many pieces do Party A and Party B need to process?
Analysis: If we follow the original ratio, A will have 24×(24÷ 12)=48 pieces per hour, and B will have 24 pieces, so there will be 22 pieces left in A at last.
There are still 130-22= 108 parts left, because 48- 12=36 parts are processed less every hour, so 108÷36=3 hours later.
So A needs to deal with12× 3+130 =166, and B needs to deal with 24×3=72.
8. Party A and Party B cooperated on a 3600-meter-long railway. When Party A completes 3/4 of its assigned tasks and Party B completes 4/5 and 40m of its assigned tasks, there are still 780m to be completed. How many meters of tasks have Party A and Party B assigned respectively?
Analysis: If both teams have completed 3/4, there is still 3600×( 1-3/4)=900 meters.
Description B's 4/5-3/4= 1/20 is 900-780-40 = 80m.
So the task of team B is 80÷ 1/20= 1600 meters, and the task of team A is 3600- 1600=2000 meters.
Super-difficult math application problems and answers 2 application problems
1. It is planned to complete a section of the road in 20 days 16 people. After five days of labor, four people will be added. If these people have the same work efficiency, how many days will the road construction task be completed ahead of schedule?
A hotel needs to install 240 air conditioners. It is known that 10 engineers and technicians can install 64 air conditioners in 8 hours. Now the hotel requires the installation company to install it within 12 hours. How many technicians with the same efficiency are needed?
3. A project was originally planned to be completed by 42 people 12 days (working 8 hours a day). After 7 days of work, 12 people were transferred to support other urgent tasks. How many days will it take to finish the remaining work? How many hours do you have to work every day if you are required to finish the work according to the original date?
Xiao Qiang lives on the third floor. It takes 60 seconds to walk from the first floor to the third floor. At this rate, how many seconds does it take to get from the first floor to the sixth floor?
5. Processing 9,600 sets of clothes, 30 people 10 day to complete 3,600 sets, adding 20 people. How many days will it take to finish the rest?
Reference answer
1. Let a person do a day job.
(1) The total workload of repairing this section is: 16×20=320 (daily workload).
(2) After five days of repair, the remaining workload is: 320- 16×5=240 (daily work).
(3) Remaining' workload (16+4) and days that people need to do: 240÷( 16+4)= 12 (days).
(4) Days in advance: 20-( 12+5) = 3 (days)
Comprehensive formula:
20-[( 16×20- 16×5)÷( 16+4)+5]
=20-[(320-80)÷20+5]
=20-( 12+5)
=3 days
2.( 1) A technician installs the air conditioner 1 hour: 64÷ 10÷8=0.8 (units).
(2) 12 hour can install 240 air conditioners, and the required technical personnel are: 240÷ 12÷0.8=25 (person).
(3) Need to increase technical personnel: 25- 10= 15 (name)
Comprehensive formula:
240÷ 12÷(64÷ 10÷8)- 10
=20÷0.8- 10
=25- 10
= 15 (name)
3. Let 1 person do a day job.
(1) The total workload of the project is 42× 12=504 (daily workload).
(2) After working for 7 days, the remaining workload is: 504-42× 7 = 504-294 = 2 10 (daily work).
(3) The remaining workload is (42- 12), and the required days are: 2 10÷(42- 12)=7 (days).
Ask the second question:
Let a person work for an hour as "working time".
(1) The remaining workload is expressed as "working time": 2 10×8= 1680 (working time).
(2) Daily workload for completion on schedule:1680 ÷ (42-12) ÷ (12-7) =11.2 (hours).
The second problem is another solution:
(1)42 people work 8 hours a day, and the working time that can be completed in one day is 42×8=336 (working time).
(2) To finish on schedule, the remaining 30 people must complete 336 working hours every day, so the working hours every day are: 336÷30= 1 1.2 (hours).
Comprehensive formula, the first question: (42×12-42× 7) ÷ (42-12) = 7 (days).
Question 2: 42×8÷30= 1 1.2 (hours)
4.
(1) It takes 60 seconds for Xiao Qiang to walk from the first floor to the third floor, so it takes 60÷2=30 (seconds) to get to each floor.
(2) The walking time from the first floor to the sixth floor is 30×(6- 1)= 150 (seconds).
5.
(1) Clothing output per person per day: 3600÷30÷ 10= 12 (sets)
(2) Remaining completion days: (9600-3600) ÷ [(30+20) ×12] =10 (days).
Comprehensive formula:
(9600-3600)÷[(30+20)×(3600÷30÷ 10)]
=6000÷[50× 12]
=6000÷600
= 10 (days)