1. The distance between the two stations is 275 kilometers. The local train goes from Station A to bilibili at a speed of 50 kilometers per hour. 1h later, the express train runs from bilibili to Station A at a speed of 75km/ h. How many hours after the local train leaves, will you meet the express train?

Set the local train to meet the express train in an hour.

50a+75(a- 1)=275

50a+75a-75=275

125a=350

A=2.8 hours

2. A car travels from place A to place B at a speed of 40 kilometers per hour. After 3 hours, due to the rain, the average speed was forced to drop 10km. The result arrived at B 45 minutes later than expected. Find the distance between a and b.

Set the original time to one hour.

45 minutes =3/4 hours

According to the meaning of the question

40a = 40×3+(40- 10)×(a-3+3/4)

40a= 120+30a-67.5

10a=52.5

A=5.25=5, 1/4 hours =2 1/4 hours.

Therefore, the distance between Party A and Party B is 40×2 1/4=2 10 km.

The locksmith class in a workshop is divided into two teams to watch the tree planting work. The number of people in Team A is twice that of Team B. If 16 people are transferred from Team A to Team B, the number of people left in Team A is three less than that of Team B. What about the original numbers of Team A and Team B?

Solution: Team B originally had A, while Team A had 2a.

Then according to the meaning of the question

2a- 16 = 1/2×(a+ 16)-3

4a-32=a+ 16-6

3a=42

a= 14

Then team B was originally 14, and team A was originally 14×2=28.

At present, team B 14+ 16=30 people, and team A = 28- 16= 12 people.

4. It is known that the profit of a store in March is 654.38+10,000 yuan, and the profit in May is1320,000 yuan. The month-on-month growth rate in May was 654.38+00 percentage points higher than that in April. Find the monthly growth rate in March.

Solution: Let April profit be X.

Then x * (1+10%) =13.2.

So x= 12.

Let the growth rate in March be y.

Then10 * (1+y) = X.

y=0.2=20%

So the growth rate in March was 20%

5. The school arranges dormitories for boarding students. If there are 7 people living in each dormitory, 6 people can't arrange it. If there are 8 people living in each dormitory, then there are only 4 people living in one dormitory, and there are 5 empty dormitories. How many people are there?

Solution: There is room A, with 7a+6 people in total.

7a+6=8(a-5- 1)+4

7a+6=8a-44

a=50

Someone =7×50+6=356 people

6. One kilogram of peanuts can fry 0.56 kilograms of peanut oil, so how much peanut oil can be fried in 280 kilograms?

Proportional solution

Suppose you can fry one kilogram of peanut oil.

1:0.56=280:a

A = 280× 0.56 = 156.8kg

Complete formula: 280 ÷1× 0.56 =156.8kg.

7. A batch of books are distributed to Class 1 10 and Class 2 15. How many books have been distributed in both classes now?

Solution: Let's assume that there are a total of books.

Class number =a/ 10

Number of Class Two =a/ 15

Then they are evenly divided into two categories, each of which is a/(a/10+a/15) =10×15/(10+15) =/kloc.

8. The tree planting team of June 1st Squadron went to plant trees. If everyone plants five trees, there are still 65,438+04 seedlings left. If each race has seven trees, there will be six fewer seedlings. How many people are there in this team? A * *, how many seedlings?

Solution: There is one person.

5a+ 14=7a-6

2a=20

a= 10

A * * * has 10 people.

There are 5× 10+ 14=64 saplings.

9. A barrel of oil weighs 50 kilograms. Half of the soybean oil poured out for the first time was less than 4 kilograms, and the remaining three-quarters were two and two-thirds kilograms more for the second time. At this time, the barrel filled with oil weighs one third of a kilogram. How much oil was there in the original barrel?

Solution: Let the oil weigh one kilogram.

Then the barrel weighs 50-a kilograms.

Pour out 1/2a-4kg for the first time, leaving 1/2a+4kg.

Pour out 3/4× (1/2a+4)+8/3 = 3/8a+17/3kg for the second time, leaving1/2a+4-3/8a-17/3 =/kloc.

According to the meaning of the question

1/8a-5/3+50-a= 1/3

48=7/8a

A = 384/7kg

There used to be 384/7kg of oil.

10, use a bundle of 96m cloth to make clothes for the students in Class 1, Grade 6, 15 use 33m cloth. According to this calculation, which class is the most suitable for these fabrics to make school uniforms? (1 class 42, class 2 43, class 3 45)

Give person a 96 meters.

According to the meaning of the question

96:a=33: 15

33a=96× 15

A about 43.6

So it is suitable for Class 2, with a surplus, but not much. It is not enough to do it for Class Three.

1 1, a fraction. If the numerator adds 123 and the denominator subtracts 163, the new fraction is 3/4; If the numerator adds 73 and the denominator adds 37, then the new score is reduced to 1/2, and the original score is found.

Solution: Add 123 to the original fractional numerator and subtract 163 from the denominator to get 3a/4a.

According to the meaning of the question

(3a- 123+73)/(4a+ 163+37)= 1/2

6a- 100=4a+200

2a=300

a= 150

Then the original score = (3×150-123)/(4×150+163) = 327/763.

12. The fruit shop sent a batch of fruits. On the first day, it sold 60 kilograms, which is exactly two-thirds of the sales the next day. In two days, it sold a quarter of the fruit. How many kilograms is this batch of fruit (equation solved)?

Suppose the fruit used to have a kilo.

60+60/(2/3)= 1/4a

60+90= 1/4a

1/4a= 150

A=600 kg

This kind of fruit used to weigh 600 kilograms.