1÷( 1/ 10+ 1/ 15)
= 1÷( 1/6)
=6 days
2. A bag of rice is eaten by Party A, Party B and Party C for 8 days, while Party A eats for 24 days and Party B eats for 36 days. How many days will Party C eat?
1÷( 1/8- 1/24- 1/36)
= 1÷( 1/ 18)
= 18 days
3. For a project, it takes 65,438+08 days for Party A to do it alone, and 65,438+05 days for Party B to do it alone. After two people do it together for six days, how many days will Party B have to do the rest?
[ 1-( 1/ 18+ 1/ 15)*6]÷( 1/ 15)
=( 1- 1 1/ 15)÷( 1/ 15)
=(4/ 15)÷( 1/ 15)
=4 days
4. For a project, it takes 12 days for Party A to do it alone and 18 days for Party B to do it alone. How many days can two people work together to complete two-thirds of the project?
(2/3)÷( 1/ 12+ 1/ 18)
=(2/3)÷(5/36)
=24/5
=4.8 days
5. To build a road, it takes 16 days for Party A to build it alone, and 24 days for Party B. If Party B builds it for 9 days first, then Party A and Party B jointly build it, how many days will it take?
[ 1-( 1/24)*9]÷( 1/ 16+ 1/24)
=(5/8)÷(5/48)
=6 days
Example 1 A can finish the work in 9 days, and B can finish the work in 6 days. Now A has done it for three days first, and B continues to finish the rest. B How many days does it take to finish all the work?
Answer: B It takes 4 days to finish all the work.
Scheme 2: The least common multiple of 9 and 6 is 18. Let the total workload be 18. Party A completes 2 copies every day, and Party B completes 3 copies every day. How long does it take Party B to complete the remaining work?
(18- 2 × 3)÷ 3= 4 (days).
Solution 3: The ratio of working efficiency of A and B.
6∶ 9= 2∶ 3.
A has done 3 days, which is equivalent to 2 days for B. It takes 6-2=4 (days) for B to finish the rest of the work.
With the cooperation of both parties, a job can be completed in 30 days. After 6 days, Party A left and Party B continued to do it for 40 days. If this work is done by Party A or Party B alone, how many days will it take?
Solution: * * * did it for 6 days.
It turns out that A does it for 24 days and B does it for 24 days.
Now, A does 0 days and B does 40=(24+ 16) days.
This shows that the work that A did in 24 days can be replaced by B in 16 days, so the work efficiency of A is high.
If b does it alone, the time required is
If A does it alone, the time required is
Answer: It takes 75 days for A to do it alone, or 50 days for B to do it alone.
A project can be completed by Party A alone for 63 days, and then by Party B alone for 28 days. If both parties cooperate, it will take 48 days to complete. Now Party A does it alone for 42 days, and then Party B does it alone. How many more days does Party B need to do?
Solution: First, compare the following:
63 days for A and 28 days for B;
A does it for 48 days and B does it for 48 days.
It is known that A needs to do 63-48= 15 (days) less, and B needs to do 48-28=20 (days) more, thus obtaining A's.
A has been doing it for 42 days, and 63-42=2 1 (day) is less than 63 days, which is equivalent to B.
So, B still has to do it.
28+28= 56 (days).
A: B It will take another 56 days.
Example 4 A project was completed by group A alone 10 day, and group B alone for 30 days. Now the two teams cooperate, during which Team A has a rest for 2 days and Team B has a rest for 8 days (neither team has a day off). How many days did it take from the beginning to the end?
Scheme 1: Team A works alone for 8 days and Team B works alone for 2 days, thus completing the workload.
The remaining workload is the cooperation between the two teams. How many days will it take?
2+8+ 1= 1 1 (days).
Answer: It took 1 1 day from the beginning to the end.
Solution 2: We assume that the total workload is 30 copies. Party A completes 3 copies every day, and Party B completes 1 copy every day. Team A works alone for 8 days, and after team B works alone for 2 days, the two teams need to cooperate.
(30-3× 8-/kloc-0 /× 2) ÷ (3+1) =1(days).
Option 3: Team A does 1 day, which is equivalent to Team B doing 3 days.
After team A did it alone for 8 days, there was still (team A) 10-8= 2 (days) workload, which was equivalent to team B's 2×3=6 (days). After doing it alone for 2 days, there was still (team B) 6-2=4 (days) workload.
4=3+ 1,
Three days can be completed by team A 1 day, so the two teams only need to cooperate 1 day.
Example 5 A project is completed by Team A in 20 days and Team B in 30 days. Now they are working together, during which Team A has a rest for 3 days and Team B has a rest for a few days. It took 16 days from start to finish. How many days did Team B rest?
Option 1: What if both teams don't rest for 16 days?
Because the workload that the two teams didn't do during the break was
The amount of work that team B didn't finish during the break was
How many days will Team B rest?
A: Team B rested for five and a half days.
Solution 2: Assume that the total workload is 60. Party A completes 3 copies every day, and Party B completes 2 copies every day.
The workload that the two teams didn't do during the break was
(3+2)× 16- 60= 20 (copies).
Therefore, B's rest day is
(20- 3 × 3)÷ 2= 5.5 (days).
Option 3: Team A does it for 2 days, which is equivalent to Team B doing it for 3 days.
Team A has a 3-day rest, which is equivalent to 4.5 days rest for Team B. 。
If Team A 16 doesn't rest, Team A will only work for 4 days, which is equivalent to Team B's working for 6 days. Team B's rest day is
16-6-4.5=5.5 (days).
Example 6 has two tasks, A and B. It takes 65,438+00 days for Zhang to complete task A alone, and 65,438+05 days for Zhang to complete task B alone. It takes 8 days for Li to complete work A and 20 days for Li to complete work B. If two people can cooperate in each job, how many days will it take to complete these two jobs?
Solution: Obviously, Li's work efficiency in doing A work is high, and Zhang's work efficiency in doing B work is also high. So let Li do A first and Zhang do B first.
Suppose B's workload is 60 copies (15 and the least common multiple of 20), Zhang completes 4 copies every day and Li completes 3 copies every day.
In another 8 days, Li will be able to finish work A. At this time, Zhang still has (60-4×8) copies of work B, which needs the cooperation of Zhang and Li.
(60-4×8)÷(4+3)=4 (days).
8+4= 12 (days).
A: It will take at least 12 days to complete these two tasks.
For a project, it takes 10 days for Party A to do it alone, and 15 days for Party B to do it alone. If two people cooperate, they will.
It takes eight days to complete the project, and the fewer days two people work together, the better. So how many days do two people work together?
Solution: Assume that the workload of this project is 30 copies, with Party A completing 3 copies every day and Party B completing 2 copies every day.
Two people cooperate, * * * to complete.
3× 0.8+2 × 0.9= 4.2 (copies).
Because two people should work together for as few days as possible, the one who works alone should be the one with high efficiency. Because it will be completed in 8 days, the number of days for two people to cooperate is
(30-3×8)÷(4.2-3)=5 (days)
Obviously, it finally became a problem of "chickens and rabbits in the same cage".
Example 8 Party A and Party B cooperate in a job. Because of their good cooperation, Party A's work efficiency is faster than when doing it alone.
How many hours will it take if this work is always done by one person alone?
Solution: what is the workload of B working alone for 6 hours?
B the workload per hour is
Two people work together for 6 hours. What does A accomplish?
A the amount of work done per hour when working alone
A How long does it take a person to do this job?
A:A It takes 33 hours for one person to finish the work.
Most examples in this section are treated as "integers". However, "integer" does not make the calculation of all engineering problems simple. This is the case in Example 8. Example 8 can also be an integer, when b is found.
It's convenient, but it doesn't do much good. There is no need to reinvent the wheel.
Example 9 A job is completed in 36 days by Party A and Party B, 45 days by Party B and 60 days by Party A and Party C. How many days does it take for Party A to complete it alone?
Solution: Let the workload of this work be 1.
The cooperation among Party A, Party B and Party C is completed every day.
Minus the work done by Party B and Party C every day, Party A will finish it every day.
A:A It takes 90 days to do it alone.
Example 9 can also be rounded off, assuming that the total workload is 180, Party A and Party B complete 5 copies per day, Party B and Party C complete 4 copies per day, and Party A and Party C complete 3 copies per day. Please have a try. Will it be more convenient to calculate?
Example 10 for a job, it takes 12 days for A to do it alone, 18 days for B to do it alone, and 24 days for C to do it alone. The work was done by A for a few days, then by B for three times as many days as A, and then by C for twice as many days as B, and finally the work was completed.
Solution: A does 1 day, B does 3 days, and C does 3×2=6 (days).
Explain that A did it for 2 days, B did it for 2×3=6 (days), C did it for 2×6= 12 (days), and three people did it together.
2+6+ 12=20 (days).
It took 20 days to finish the work.