Solve six math problems

1. The reporter rode a bicycle from place A to place B, which are 72 kilometers apart, and performed the task within the specified time. When he walked half the distance, his superior informed him that he should arrive 1 hour earlier, so he walked 3 kilometers more every hour and asked the reporter how many kilometers he walked every hour.

Solution: Suppose the original journey is one kilometer per hour, and the second half of the journey is a+3 kilometers per hour.

Half distance = 1/2×72 = 36 km.

36/a-36/(a+3)= 1

36(a+3)-36a=a？ +3a

Answer? +3a- 108=0

(a+ 12)(a-9)=0

A=9 or a=- 12.

So I used to walk 9 kilometers per hour.

2. In June this year, a city adjusted the residents' water price by 5438+ 10/,and the water fee per cubic meter increased by 25%. The water fee of Xiaoming's family in June 5438+February last year was 18 yuan, while the water fee in May this year was 36 yuan. It is known that the water consumption of Xiaoming's family in May this year was 6 cubic meters more than that in June 65438+February last year. Seek the price of water for residents in this city.

Solution: Suppose the price of water fee is A yuan/cubic meter this year and the water consumption is B cubic meter this year.

Then last year's water fee per cubic meter was a/( 1+25%)=4/5a.

B-6 cubic meters of water was used in February last year.

4a/5×(b-6)= 18( 1)

ab=36(2)

Replace (2) with (1)ab-6a=22.5.

36-6a=22.5

A=2.25 yuan

This year's water fee is 2.25 yuan/cubic meter.

A garment factory will process 300 sets of garments. After processing 60 sets, new technology is adopted, and the daily work efficiency is doubled. As a result, it takes 9 days to complete the task. How many sets of clothes are processed in this factory every day?

Suppose a set is processed every day, and then 2a sets are processed every day.

60/a+(300-60)/(2a)=9

120+240= 18a

18a=360

a=20

I used to handle 20 sets every day.

4. Graduation is coming. Several good students are going to a place to play together after the senior high school entrance examination. The estimated cost of * * * is 1.200 yuan. Later, two students joined, but the total cost remained the same. Each student could share 30 yuan less and try to find out the number of people who originally planned to play together.

Solution: Let's say that there are A people taking part in the tour, and then there are a+2 people.

Originally everyone shared 1200/a, but later everyone shared 1200/(a+2).

According to the meaning of the question

1200/a- 1200/(a+2)= 30

1200 a+2400- 1200 a = 30a？ +60a

Answer? +2a-80=0

(a+ 10)(a-8)=0

A=8 or-10 (omitted)

The test shows that a=8 is the root of the equation.

So the original plan was eight companions.

5. Xiaoli and Xiaoxue set out from A and B at the same time, face to face, and immediately returned to their original places after meeting, each taking 48 minutes. If Xiaoxue leaves 10 minutes earlier than Xiaoli, how long will it take for Xiaoli to meet Xiaoxue 20 minutes after departure, for Xiaoli to go from A to B and for Xiaoxue to go from B to A?

Solution: It took 48/2=24 minutes to start at the same time and meet each other.

When we met for the second time, Xiaoli walked for 20 minutes and Xiaoxue spent 30 minutes.

Xiaoxue's 10 minute journey is 4 minutes for Xiaoli to meet for the first time and 6 minutes for Xiaoxue herself.

So Xiaoli walks 10-6=4 minutes, and Xiaoxue needs 10-(24-20)=6 minutes.

So the distance ratio of the first encounter = inverse ratio of time = 6: 4 = 3: 2.

When we first met, Xiaoli walked 3/5 of the whole journey. Xiaoxue walked 2/5 of the whole journey.

Xiaoli needs 24/(3/5)=40 minutes from A to B.

It takes 24/(2/5)=60 minutes for light snow to travel from B to A.

6. A school organizes class A and class B students to participate in the voluntary labor of "beautifying the campus". If Class A works for 2 hours and Class B works for 3 hours, it just completes half of all the work; If Class A works 3 hours and Class B works 6 hours, it just completes 7/8 of all the work. How long will it take each class to finish this work alone? A 2 hours and B 3 hours to complete all 1/2.

Then A 2×3/2=3 hours, B 3×3/2=9/2 hours to complete all 1/2×3/2=3/4.

So it takes 6-9/2=3/2 hours for B to complete 7/8-3/4= 1/8.

So the work efficiency of B is (1/8)/(3/2) =112.

A's work efficiency = (1/2-112× 3)/2 =1/8.

So it takes a person1(1/8) = 8 hours to complete it.

It takes1(112) =12 hours.

Or: Let A's work efficiency be A and B's be B.

2a+3b= 1/2( 1)

3a+6b=7/8(2)

( 1)×2-(2)

a= 1/8

b= 1/ 12