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Mathematical problems in life
14, a project, a team of 20 people do it alone for 25 days. If it takes 20 days to complete, how many people need to be added?

Solution: Take everyone's workload as the unit 1.

It is also necessary to increase/kloc-0 /× 25× 20/(/kloc-0 /× 20)-20 = 25-20 = 5 people.

15. For a project, Party A will do it for 3 days first, and then Party B will join in. Two-thirds of the projects completed after 4 days are 1 and three-quarters of the projects completed after 10. A was transferred because of some things, and B did the rest. How many days did a * * * do?

Solution: according to the meaning of the problem

The cooperation between Party A and Party B began in 4 days13 and ended in 3/4 days 10.

So the cooperation between Party A and Party B is10-4 = 3/4- 1/3=5/ 12 in 6 days.

Therefore, the work efficiency of both parties is =(5/ 12)/6=5/72.

Then the working efficiency a = (1/3-5/72× 4)/3 = (1/3-5/18)/3 =1/54.

Party B's work efficiency = 5/72-1/54 =11/216.

Then B needs to complete the remaining (1-3/4)/(11/216) = 54/11day.

A * * * made 3+10+54/1=17 and10//day.

16, both parties made the same parts. /kloc-After 0/6 days, Party A needs 64 B and 384 B to complete it. The work efficiency of Party B is 40% less than that of Party A, so how can we find the efficiency of Party A?

Solution: Let the working efficiency of A be A/ day, and then B be (1-40%)A = 0.6a/ day.

According to the meaning of the question

16a+64=0.6a× 16+384

16×0.4a=320

0.4a=20

A=50/day

A's work efficiency is 50/ day.

Arithmetic method:

B does 40% less than A every day.

Then 16 days is 384-64= 320 less.

Do 320/ 16 = 20 less every day.

Then the working efficiency of A = 20/40% = 50/ day.

17, Master Zhang has a rest every six days 1 day, and Master Wang has a rest every five days for two days. For an existing project, Master Zhang needs 97 days and 75 days. If two people cooperate, how many days does a project take?

Solution:

97 divided by 7 equals 13, leaving 6 13 * 6 = 78, 78+6 = 84 working days.

75 divided by 7 equals 10,5,10 * 5 = 50,50+5 = 55 working days.

Master Zhang completes 1/84 every working day and 6/84 =114 every week.

Master Wang completes 1/55 every working day and 5/55 =11/every week.

Two people work together to complete 139/4620 every working day and 25/ 154 every week.

Six weeks to complete 150/ 154, leaving 4/ 154.

(4/ 154)/( 139/4620)= 120/ 139

So, six weeks and one day, 43 days.

18, Party A, Party B and Party C jointly complete a project, and complete it all in three days15. Then Party A rested for three days, Party B rested for two days, and Party C didn't rest. If Party A's workload is three times that of Party C and Party B's workload is four times that of Party C, how many days will it take to complete the work from scratch?

Solution: The sum of the working efficiencies of A, B and C = (1/5)/3 =115.

Work efficiency c = (115)/(3+4+1) =1120.

A's work efficiency =1120× 3 =1/40.

Party B's work efficiency =1120× 4 =1/30.

Here, the working efficiency of C is regarded as a multiple of 1.

A rest for 3 days, B rest for 2 days, and a * * * is finished.

1/30+ 1/ 120×3=7/ 120

Then the remaining needs (1-1/5-7/120)/(115) = 89/8 days.

A * * * takes 3+3+89/8= 17 and 1/8 days.

19. Party A works alone for 30 days and Party B works alone for 20 days. After Party A works alone for a few days, Party B takes over, Party A works alone for 22 days, and Party A works alone for several days.

Solution: work efficiency B = 1/20.

B Completed in 22 days1/20× 22 =1110.

Complete1110-1=1/kloc-0.

The work efficiency difference between Party B and Party A =1/20-1/30 =1/60.

So A did (110)/(1/60) = 6 days.

B did it for 22-6= 12 days.

Considering that chickens and rabbits are in a cage.