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Who has the problem and answer of fractional equation?
During the Spring Festival transportation in 2008, a large-scale ice and snow disaster occurred in the south of China, resulting in the power failure of a certain place. The local power supply bureau organized electricians to carry out emergency repair. The power supply bureau was 15 kilometers away from the emergency repair site. The emergency repair vehicle was loaded with the required materials. First, the electricians started from the power supply bureau, and 15 minutes later, the electricians started from the same place by jeep car, As a result, they arrived at the repair site at the same time. It is known that the speed of the jeep is 1.5 times that of the repair vehicle
Analysis: this problem is a fractional equation application problem based on the southern snow disaster and the power supply bureau organizing electricians to repair the power-off circuit. It involves three quantities: distance, time and speed, and satisfies the relationship: distance = time × speed. Suppose the speed of the repair vehicle is XKM / h, then the speed of the jeep for electricians is 1.5xkm/h. The quantitative relationship is analyzed as follows:
\X05 emergency repair vehicle
Distance
Speed
Time
According to the meaning of the problem, the repair vehicle takes more hours than the jeep
If the speed of the repair vehicle is km / h, the speed of the jeep is km / h
From the meaning of the title,
.
The solution is
After testing, it is the solution of the original equation, and all accord with the meaning of the problem
A: the speed of the rush repair car is 20 km / h, and that of the jeep is 30 km / h
Due to various factors, the market price of pork is still rising. According to the survey, the price of grade I pork in May this year is 1.25 times that in January. Xiaoying's mother also bought grade I pork in May with 20 yuan, which is 0.4 Jin less than that in January. So how much is the price of grade I pork in January this year?
Analysis: the application of fractional equation in the background of rising prices involves three quantities: unit price, quantity and total price, which satisfies the following equation: total price = unit price × quantity. According to Xiaoying's mother, she also uses 20 yuan to buy grade I pork in May, which is 0.4 Jin less than grade I pork in January, as the selection relationship, and then solves the equation
Suppose that the price of first-class pork in January this year is yuan per catty,
According to the meaning of the title:
The solution is as follows
The test shows that it is the solution of the original equation
A: the price of first grade pork in January this year is 10 yuan per catty
Example 3. Class A and class B play the game of "holding the ball in a race". They agree to start from the starting line with a racket holding the table tennis ball, and run back to the starting line by bypassing point P (as shown in the figure). When the table tennis ball falls down on the way, they have to pick it up and go back to the place where it fell off to continue the race. The winner is the one who takes less time, A classmate said: "the sum of all the time we spent is 50 seconds", B said: "when the process of picking up the ball is not included, a's speed is 1.2 times as fast as mine". According to the graphic information, which classmate wins?
Analysis: this problem is based on the background of playing the game of "pitching the ball race". The key to solve the problem is to get the information from the dialogue and graphics, and extract the equivalent relationship. The idea of solving the problem is to find out the speed of a and B first, and then calculate the time of a and B to judge which student wins
Let B's speed be m / s, then a's speed is m / s,
According to the meaning of the title,
It's a good solution
After testing, it is the solution of the equation and conforms to the meaning of the problem
The time spent by student a is: (seconds),
The time used by Student B is: (seconds)
Student B won
In order to help the people in the disaster area rebuild their homes, the students of a certain school actively donate money. It is known that the total amount of the first donation is 9000 yuan, and the total amount of the second donation is 12000 yuan. The average amount of donations in the two times is equal, but the number of people who donate money in the second time is 50 more than that in the first time
The first per capita contribution = the second per capita contribution
If the second donation number is people, then the first donation number is people
According to the meaning of the problem, we can solve this equation
After testing, it is the root of the listed equation and conforms to the meaning of the question
A: the number of the second donation is 200
Example 6 in the resettlement work of the victims of the "great earthquake", an enterprise received a batch of tasks to produce 24000 type a plates and 12000 type B plates. It is known that the enterprise has arranged 140 people to produce these two kinds of plates, and each person can produce 30 type a plates or 20 type B plates every day, To ensure that they use the same time to complete their respective production tasks?
Analysis: the production time of type a plate is equal to the production time of type B plate,
The solution is as follows
After testing, it is the root of the equation and conforms to the meaning of the question
Answer: should arrange 80 people to produce a kind of board, 60 people produce B kind of board
Example 7 a train of a Railway Bureau received the task of delivering disaster relief materials to the disaster area of Sichuan, 720 kilometers away. When it reached 120 kilometers away from its destination, it was forced to stop for 30 minutes due to the repair of the section damaged by the earthquake in front of it. After it started again, the speed increased to 1.5 times of the original speed, which just delivered the goods on time and calculated the original speed of the train
Let the original speed of the train be x km / h and then 1.5 x km / h
The solution is x = 80
After testing, x = 80 is the root of the equation, and in line with the meaning
A: the original speed of the train was 80 km / h
If Party A does it alone, it will be completed on schedule; if Party B does it alone, it will take more than six months to complete it. Now Party A and Party B work together for four months, and the rest will be completed by Party B, it will be completed on schedule
Analysis: how long does it take for the project to be completed? If it takes x months to complete the project, then it will take x months for team a to do it alone, and X + 6 months for team B to do it alone. If the quantity of the project is regarded as 1, then the efficiency of Party A is 1 / X and that of Party B is 1 / (x + 6)
The equation is as follows:
[1/x+1/(x+6)]*4 + (x-4)/(x+6)= 1
(8x+24)/x(x+6) + (x^2-4x)/x(x+6) =1
8x+24+x^2-4x=x(x+6)
4x+24+x^2=x^2+6x
24=2x
x=12
A: it was originally stipulated that the project would be completed in December
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