1. It takes 10 days for Party A to complete a project, 15 days for Party B, and 20 days for Team C. Team A left because of something. It took six days. How many days did Team A actually do it?
Solution: the sum of the work efficiency of B and C =
B and c both do it for 6 days and finish it.
A all done.
So A really did it.
2. Master Zhang has a rest every 6 days 1 day, and Master Wang has a rest every 5 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 equals10,5,10× 5 = 50,50+5 = 55 working days.
Master Zhang finishes it every working day and every week.
Master Wang finishes it every working day and every week.
The cooperation between two people is completed every working day and every week.
Six weeks to complete, remaining time
So, six weeks and one day, 43 days.
3, a project, a team of 20 people 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 1÷(25×20)×20-20=25-20=5 people.
4. Put a small cube with a side length of 4 decimeters on a cube with a side length of 5 decimeters (right), and find the surface area of this three-dimensional figure.
The surface area of this three-dimensional figure is 2 14 square decimeter.
Analysis: We imagine that the small cube above can be "compressed" downward. After "compression", we find that the upper surface of the small cube and the shadow part in the upper surface of the big cube are combined together, just above the big cube. In this way, the surface area of this three-dimensional figure can be divided into two parts:
Up and down direction:
Two bottom faces of a big cube:
5×5×2=50 (square decimeter)
Side:
Four sides of a small cube and four sides of a big cube.
5×5×4= 100 (square decimeter)
4×4×4=64 (square decimeter)
The surface area of this three-dimensional figure is:
50+ 100+64=2 14 (square decimeter)
The expressway under construction should be invited for bidding. There are two engineering teams, Team A and Team B. If the two teams cooperate, it can be completed in 24 days. The cost is 6.5438+0.2 million yuan; If Party A works alone for 20 days, the remaining works will be done by Party B, which will take 40 days to complete, and it will cost 165438+ ten thousand yuan. Q:
(1) How many days will it take for Team A and Team B to finish this project alone?
(2) How much did Team A and Team B spend to complete this project alone?
Solution: The sum of work efficiency of both parties =
Completed in 20 days ×20=
Work efficiency B =( 1-)⊙(40-20)= 1
B It takes 1÷= 120 days to complete it alone.
A's work efficiency =-=
A It takes one person 1÷=30 days to complete.
(2) Party A and Party B need120 ÷ 24 = 50,000 yuan for one day's work.
Cooperation for 20 days needs 5× 20 = 1 ten thousand yuan.
B Working alone for 20 days needs110-100 = 65438+ten thousand yuan.
B One day's work needs 10÷20 = 0.5 million yuan.
Then A needs 5-0.5 = 45,000 yuan for a day's work.
A alone needs 4.5× 30 = 1.35 million yuan.
B alone needs 0.5×120 = 600,000 yuan.