Analysis: The weight of the three mixed solutions is1000+100+400 =1500g, and the alcohol content is14% ×1500 = 210g, while the original.
Since the concentration of A is twice that of B, the alcohol content of 400g solution B is equivalent to 400g solution A = 200g, so the concentration of solution A is 60÷( 100+200)=20%.
2. A store spends the same money on three different kinds of candy, namely, A, B and C. It is known that the price of A, B and C per kilogram is 9.60 yuan, 16 yuan and 18 yuan respectively. If these three kinds of candy are mixed into assorted candy, and the price is 20% profit, then what is the price of this assorted candy per kilogram?
Analysis: 3 ÷ (1/9.6+1118) × (1+20%) =1.
There are slopes from a to b, both uphill and downhill. It takes 4.5 hours for someone to ride a bicycle to and from A and B. If it is known that the speed of this person is 12 km/h when going uphill and 18 km/h when going downhill, what is the total length of A and B?
Analysis: The uphill return just broke down, so it takes 36÷ 12+36÷ 18=5 hours to go back and forth to 36 km * *, so 1 hour can go back and forth to 36÷5=7.2 km. 4.5 hours can be 7.2×4.5=32.4 kilometers.
4. For a project, Party A needs 1 hour for 36 minutes, and Party B needs 1 hour for cooperation. Now, after Party A has completed 65,438+0/65,438+02, both parties will work together, but all the work will take 65,438+0 hours and 38 minutes to complete due to Party A's midway rest.
Analysis:
Solution: What B does in 1 hour is equivalent to what A does in 36 minutes, and the efficiency ratio of B to A is 36: 60 = 3: 5.
A112 takes112× 96 = 8 minutes.
Later it took 98-8=90 minutes. If 90 minutes is 90÷60=3/2, it is actually 3/2-(1-112) = 7/12, which means that A has a rest period.
This period of time is completed by B alone, and 7/ 12×3/5=7/20 can be completed.
5. Let A, B and C walk around the campus in the same direction at a certain speed for 6 minutes, 7 minutes, 1 1 minute. After starting from the starting point A, B starts 1 minute later than A, and C starts 5 minutes later than B, then A, B and C pass at the same time for the first time, and the starting point is A.
Analysis: According to the conditions, when C set out, A just drove for 5+ 1=6 minutes, that is, when A and C passed the starting point at the same time, it was 6× 1 1=66 minutes late.
Since B takes 7-5=2 minutes, it means that the multiple of 66 should be divided by more than 7 minutes. When 66×3= 198 minutes, 198 ÷ 7 = 28...2 minutes, the condition is satisfied.
Therefore, the first simultaneous departure place of ABC is 6+ 198=204 minutes after the departure of A.
6. Students in a class are divided into several groups to plant trees. If each group plants n trees, and n is a prime number, there are 20 seedlings left. If each group plants 9 trees, there are still 2 trees missing. How many groups are the students in this class divided into?
Analysis:
Solution: It can be seen that n is a prime number less than 9, and the difference is 20+2=22.
Explain that the group number is a divisor of 22, and 9-N is also a divisor of 22.
9-N is less than 1 1, so 9-N=2.
So the number of groups is 22÷2= 1 1 group.
7. The school held a computer Chinese character input skill competition. The original selection of the first prize 15 people, the second prize of 20 people. Now the last five people in the first prize are adjusted to the second prize, so the average speech speed of the first prize winner has increased by 8 words/minute, and the average speech speed of the second prize winner has increased by 6 words/minute. So the average speed of the first prize is much less than that of the second prize?
Analysis: The average score of the first prize is 8×( 15-5)÷5= 16 words higher than these five people.
It turns out that the average score of the second prize is 6×(20+5)÷5=30 words lower than the average score of these five people.
Then the average score of the first prize is higher than that of the second prize 16+30=46 words.
8. Hong Guang Farm was scheduled to pick up shift 60 1 at 9: 00. In order to gain time, at 8: 00, the students walked from school to the farm. On the way, they met the car that picked them up on time, so they went to the farm by bus, 12 minutes earlier than the scheduled time. Cars travel 48 kilometers per hour, and students walk at a speed of several kilometers per hour.
Analysis: The walking distance of students, bus time 12÷2=6 minutes, that is to say, the students were picked up 6 minutes before 9: 00, that is, 8: 54, which means the students traveled for 54 minutes. So the speed of the car is 54÷6=9 times that of walking, so the speed of walking is 48÷9= 16/3 kilometers per hour.
9. The road between A and B is 74 kilometers long. At 8: 0015, one car went from a to b, half an hour later, another car with the same speed went from a to b, and uncle Wang set off from b by motorcycle at 8: 25. Five minutes before 9: 00, he met the first car, 9: 0016.
According to the meaning of the question, 40 points for a car, 30 points for a motorcycle are 74 kilometers, 3 1 minute for a car and 5 1 minute for a motorcycle are 74 kilometers.
We can know that driving for 40-3 1=9 minutes is equivalent to riding a motorcycle for 5 1-30=2 1 minute.
It can be concluded that it takes 40÷9×2 1+30=370/3 minutes for the motorcycle to finish running.
So the motorcycle hour is 74 ÷ 370/3× 60 = 36km.
10. In a cuboid container with a square base of 60 cm, a quadrilateral iron bar with a square base and a side length of 15 cm is erected. At this time, the water in the container is half a meter deep Now, lift the iron bar up slightly by 24 cm. How long is the wetted part of the quadrilateral cutting rod exposed to the water?
Analysis: If the volume of a 24 cm iron bar is reduced, the water surface will drop by 24×15×15 ÷ (60× 60) =1.5 cm. So1.5+24 = 25.5cm is exposed to water.