Current location - Training Enrollment Network - Mathematics courses - The sixth grade Olympic math problem is urgent ~ ~
The sixth grade Olympic math problem is urgent ~ ~
1. The transport team sent a car to transport a batch of wood. After four trips, there are still 20 cubic meters of wood left, and after two trips, the remaining wood accounts for 25% of the total. If this car carries the same amount every trip, how many cubic meters of wood is there?

Solution: Because after (4+2) passes, the remaining wood accounts for 25% of the total.

Therefore, there are (4+2) trips in total (1-25%).

Therefore, * * * needs (4+2) ÷ (1-25%) = 8 times.

In other words, it takes (8-4) trips to transport the "remaining 20 cubic meters of wood".

Therefore, * * has: 20 ÷ [(4+2) ÷ (1-25%)-4] × [(4+2) ÷ (1-25%) = 40 cubic meters.

2. To build a section of road, it takes 40 days for team A and 24 days for team B.. Now the two teams are working at the same time, and the result is to meet at a distance of 750 meters from the midpoint. How long is this road?

Solution: team a's efficiency 1/40, team b's efficiency 1/24.

Cooperation requirements:1÷ (1/40+1/24) =15 days.

After 15 days, Party A repairs 1/40× 15=3/8, and Party B repairs 1/24× 15=5/8.

Meeting at a distance of 750m from the midpoint means that B is 750× 2 =1500m longer than A..

B is 5/8-3/8 longer than A =1/4.

Therefore: total length: 1500 ÷ 1/4 = 6000m.

3. Two people, Party A and Party B, can complete nine eightieth of the project every day. If Party A works alone for eight days and Party B does it alone, it will take 10 days. How many days does it take for Party A and Party B to work alone?

Solution: The sum of the work efficiency of both parties is 9/80.

Let the working efficiency of A be X, then the working efficiency of B is 9/80-X..

Therefore: 8x+ 10×(9/80-x)= 1.

Therefore: x =116, 9/80-x= 1/20.

That is, it takes 16 days for Party A to do it alone, and 20 days for Party B to do it alone.

4. A project needs to be completed in 6 days, 9 days and 65,438+05 days. How many days does it take for Party A, Party B and Party C to cooperate now?

Solution: The cooperation between Party A and Party B takes 6 days to complete, so the sum of work efficiency of both parties is 1/6.

So the sum of ergonomics of B-C is 1/9, and that of A-C is115.

Therefore, the sum of the working efficiencies of A, B and C is (1/6+1/9+115) ÷ 2 = 31180.

Therefore, the tripartite cooperation between Party A, Party B and Party C needs1÷ 3180 =180/31day.