Solution: 7 *18-6 *19 =126-114 =12.
6* 19-5*20= 1 14- 100= 14
The two numbers removed are 12 and 14, and their product is 12* 14= 168.
10. There are seven numbers in a row, and their average value is 30, the average value of the first three numbers is 28, and the average value of the last five numbers is 33. Find the third number.
Solution: 28× 3+33× 5-30× 7 = 39.
1 1. There are two groups of numbers, the sum of the first group of nine numbers is 63, the average value of the second group is 1 1, and the average value of all the numbers in the two groups is 8. Q: How many numbers are there in the second group?
Solution: If there are X numbers in the second group, then 63+ 1 1x = 8× (9+x), and x=3.
12. Xiaoming took part in six tests, and the average score of the third and fourth tests was 2 points higher than the previous two and 2 points lower than the latter two. If the average score of the last three times is 3 points higher than the previous three times, how many points is the fourth time higher than the third time?
Solution: The third and fourth scores are 4 points more than the first two scores, and the last two scores are 4 points less. It can be inferred that the last two scores are 8 points more than the first two scores. Because the sum of the last three times is 9 points more than the sum of the first three times, the fourth time is 9-8 = 1 (points) more than the third time.
13. Mom goes to the grocery store every four days and to the department store every five days. How many times does mom go to these two stores every week on average? (expressed in decimal)
Solution: Walk 9 times every 20 days, 9÷20×7=3. 15 (times).
The ratio of the average value of 14.B and c to a is13: 7. Find the ratio of the average value of a, b and c to a. ..
Solution: If the number of A is 7, then the number of B and C is * * * 13× 2 = 26 (copies).
So the average value of a, b and c is (26+7)/3= 1 1 (copies).
So the ratio of the average of A, B, C and A is 1 1: 7.
15. The fifth-grade students participated in the pasting of cartons in the school-run factory, with an average of 76 per person. It is known that each student has at least 70 posts, and one student has 88 posts. If you don't count this classmate, then each classmate has an average of 74 posts. What is the maximum number of students who can paste the fastest?
Solution: When counting the students who posted 88 cartons, because he is 88-74 = 14 more than the average of other students, the average number of students has increased by 76-74 = 2 (one), which means that the total number of students is 14 ÷ 2 = 7 (people). So the students who posted the fastest posted the most.
74× 6-70× 5 = 94 (pieces).
16. Class A and Class B had a cross-country marching competition. Class A runs half the distance at a speed of 4.5 km/h and the other half at a speed of 5.5 km/h; During the competition, Class B travels at a speed of 4.5 km/h half the time and at a speed of 5.5 km/h the other half. Q: Who will win Class A or Class B?
Solution: The longer you walk, the shorter it takes. The fast walking distance of Class A is the same as the slow walking distance, and the fast walking distance of Class B is longer than the slow walking distance, so Class B wins.
17. It takes 3 days for the boat to go from city A to city B, and 4 days from city B to city A. How many days does it take to put an unpowered raft from city A to city B?
Solution: It takes 3 days for a boat to go downstream and 4 days for a boat to go upstream, that is to say, the boat travels in still water for 4-3 = 1 (days), which is equal to 3+4 = 7 (days) of the current, that is, the speed of the boat is 7 times of the current. Therefore, the three-day trip of the ship is equal to the 3+3× 7 = 24 (days) trip of the current, that is, it takes 24 days for the raft to drift from city A to city B.
18. Xiaohong and Xiao Qiang started from home at the same time and walked in opposite directions. Xiaohong walks 52 meters per minute and Xiao Qiang walks 70 meters per minute. They meet on the way. If Xiaohong leaves four minutes early and the speed remains the same, and Xiao Qiang walks 90 meters every minute, then the two will still meet at point A. How many meters away is Xiaohong from Xiao Qiang's home?
Solution: Because Xiaohong's speed and meeting place remain the same, Xiaohong's time from departure to meeting is the same twice. In other words, Xiao Qiang walked four points less than the first time. pass by
(70× 4) ÷ (90-70) = 14 (minutes)
It can be seen that Xiao Qiang left for the second time 14, and it is inferred that he left for the first time 18, and their homes were separated.
(52+70) × 18 = 2 196 (m)。
19. Xiaoming and Xiaojun start from A and B at the same time and go in opposite directions. If two people go at the original speed, meet at 4 o'clock; If both are faster than the original speed 1 km/h, meet at 3 o'clock. How many kilometers is it between A and B?
Solution: per hour 1 km, two people walked 6 km at 3 o'clock, which is equivalent to the distance that two people walked at the original speed 1. So the distance between A and B is 6× 4 = 24 (km).
20. Party A and Party B practice running along the 400-meter circular track, and both sides run in opposite directions from the same place on the track at the same time. After the encounter, the speed of A increased by 2m/s, and the speed of B decreased by 2m/s, so that they all returned to their original places within 24 seconds. Find the original velocity of a.
Solution: Because the speed sum of A and B is the same before and after meeting, it takes 24 seconds for them to run a circle together after meeting, so it takes 24 seconds for them to run a circle together before meeting, that is, they meet in 24 seconds.
Suppose A originally ran x meters per second, and then ran (x+2) meters per second after meeting. Because A ran back and forth for 24 seconds and * * ran 400 meters, there is 24x+24 (x+2) = 400, and the solution is x=7, 1/3 meters.
2 1. Two cars, A and B, are driving in opposite directions from two stops A and B on the expressway at the same time. It is known that the speed of car A is 1.5 times that of car B, and the time for car A and car B to arrive at station C is 5: 00 and 16: 00 respectively. When did the two cars meet?
Solution: 9: 24. Solution: It takes 16-5 = 1 1 (hours) for a car to get to station C ... When the second car is driving at 1 1, it takes1.
22. An express train goes in the opposite direction to a local train. The length of the express train is 280 meters and the length of the local train is 385 meters. The time for people sitting on the express train to see the slow train pass is 1 1 sec, so how many seconds does it take for people sitting on the slow train to see the express train pass?
Solution: The speed at which people on the express train see the local train is the same as the speed at which people on the local train see the express train, so the ratio of the length of the two cars is equal to the ratio of the time when the two cars pass by, so the required time is 1 1.
23. Party A and Party B practice running. If Party A lets Party B run 10 meter first, Party A can catch up with Party B after running for 5 seconds; If B runs 2 seconds ahead of A, A can catch up with B in 4 seconds. Q: How many meters do two people run per second?
Solution: The speed difference between Party A and Party B is 10/5=2.
The speed ratio is (4+2): 4 = 6: 4.
So A runs 6 meters per second and B runs 4 meters per second.
24.A, B and C run from A to B at the same time. When a runs to b, b is 20 meters away from b and c is 40 meters away from b; When B ran to B, C was 24 meters away from B. Q:
(1) How many meters are there between A and B?
(2) If it takes 24 seconds for C to run from A to B, what is the speed of A?
Solution: Solution: (1) When B ran the last 20 meters, C ran 40-24 = 16 (meters), the speed of C.
25. On a road, Xiaoming and Xiaoguang ride bikes in the same direction. Xiaoming rides a bike three times as fast as Xiaoguang. Every 10 minute, a bus passes by Xiaoguang, and every 20 minutes, a bus passes by Xiaoming. It is known that a bus will leave the departure station at the same time every time. Q: What is the interval between two adjacent cars?
Solution: Let the vehicle speed be A and the vehicle speed of Xiaoguang be B, then Xiaoming's cycling speed is 3b. According to the catch-up problem "catch-up time × speed difference = catch-up distance", the equation can be listed.
10(a-b)=20(a-3b)，
The solution is a = 5b, that is, the vehicle speed is five times that of low light speed. Xiaoguang walks 10 point, which is equivalent to the dealer's 2 points. Every 10 minute, a car passes through Xiaoguang, and a car is sent every 8 minutes.
26. A hare escaped 80 steps before the hounds caught up with it. Rabbits run 8 steps, hounds only need to run 3 steps, hounds run 4 steps and rabbits can run 9 steps. How many steps does a hound have to run to catch up with a hare?
Solution: The distance of dog running 12 step is equal to the distance of rabbit running 32 steps, and the time of dog running 12 step is equal to the time of rabbit running 27 steps. Therefore, for every 27 steps the rabbit runs, the dog catches up with 5 steps (rabbit step), and the dog needs to run 80 steps (rabbit step) = 180.
180/60=3
The next time is 3 pm.
93. A number is divided by 3 and 2, and then by 4, 1. Q: What is this number divided by 12?
Solution: The number of 2 divided by 3 is 2, 5, 8, 1 1, 14. . . . . .
1 divided by 4 is 1, 5, 9,. . . . .
So this number is divided by 12, and the rest is 5.
94. 16 is divided into several natural numbers, and the product of these natural numbers is required to be as large as possible. How to divide it?
Solution: 16=3+3+3+3+2+2.
The product is 3*3*3*3*2*2=324.
95. Xiaoming counts off 1 ~ 3, Xiaohong counts off 1 ~ 4. The two of them began to report at the same speed. When both of them reported 100, how many times did they report the same number?
Solution: Every 12 times is a cycle.
1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 4 1 2 3 4 1 2 3 4
The number of two people who report three times per cycle is the same.
100= 12*8+4
So two people 8*3+3=27 times is the same.
96. A natural number plus 10 or minus 10 is a square number. Find this natural number.
Solution: let this number be X.
x+ 10=m^2
x- 10=n^2
m^2-n^2=20 (m+n)(m-n)=20
m=6，n=4
So x = 6 2- 10 = 26.
97. It is known that a railway bridge is 1000 meters long and a train passes through it. It is actually measured that it takes 120 seconds for the train to get off the bridge completely, and the time for the whole train to stay on the bridge completely is 80 seconds. Find the speed and length of the train.
Solution: The distance traveled by 120 seconds is the length of the bridge+the length of the vehicle.
The distance traveled in 80 seconds is the length of the bridge-the length of the vehicle.
So 80( 1000+ conductor) = 120( 1000- conductor)
Vehicle length = 200m.
The train speed is 10 m/s.
98. Party A and Party B practice running clockwise along the circular track. It is known that Party A needs 12 for one run and 15 for Party B for one run. If they start from both ends of the ring track at the same time, how many points will A catch up with B after starting?
Solution: (1/2)/(12-11/5) = (1/2)/(1/60).
99. Party A and Party B play table tennis and win three out of five games. It is known that A won the first game and finally won. Q: How many possibilities are there for winning or losing each game?
Solution: Armor
Jia Jia Jia Jia
a，B，B。
Jiayi Jia Jia
A，B，A，B。
A, B, A, B.
After enumeration, it is found that * * * has six possibilities.
100. Party A and Party B can process 54 parts in 2 hours * *, and Party A processes 4 parts more than Party B processes 4 times. Q: How many parts are processed per hour?
Solution: Party A and Party B can process 27 parts in one hour.
Suppose A processes X pieces per hour, then B processes 27-x pieces per hour.
According to the conditions, 3x=4(27-x)+4.
7x= 1 12 x= 16
A: A processes 16 parts per hour.