The sixth grade math application problem (1) 1. There are two beetles, red and blue, at the point A of the square ABCD with the side length of17m. At 9 o'clock, crawl along the edge at the same speed. The red beetle consists of a-b-c-d; The blue beetle is composed of A-D-C. At 9: 30, the red beetle climbs to point E, which is 5 meters away from point A 10 between AB, and then continues to climb forward, reaching point F between BC at/kloc-0:15, and then climbs forward through point C. The blue beetle climbs to point G, which is 5 meters away from point D between AD, and has a rest. When two beetles meet at the H point on the CD, it happens that the area of the quadrilateral EFHG is half that of the square. How long did the blue beetle stay at the G-spot?
2. Students 15, each student has a number, from 1 to 15. 1 wrote a five-digit number. Classmate No.2 said that "this number is divisible by 2" and classmate No.3 said that "this number is divisible by 3". Classmate No.4 said, "This number can be divisible by 4"; 15 students said that "this number can be divisible by 15". 1 students checked one by one, only two students with serial numbers were wrong, and the others were right. (1) What are the serial numbers of the two incorrect students? (2) What is the minimum value of this five-digit number?
3. Party A and Party B start from the two vertices A and C opposite to the square pool ABCD with the circumference of 1600 meters and walk around the edge of the pool in the direction of A-B-C-D-A. The speed of A is 50 meters per minute and the speed of B is 46 meters per minute. When did A and B walk on the same side for the first time? How many minutes did you walk on the same side for the first time?
4. There are 15 stops (including the starting point and the ending point) on a bus line. Anyone who gets on the bus at each stop will get off at each stop in the future. How many seats should there be in the car for passengers to use in order to make every passenger have a seat during driving?
A boat went upstream, and someone on board threw a kettle under the bridge and it was washed away by the water. When the ship turned back, it was already 20 minutes. Later, the kettle was chased 2 kilometers downstream of the bridge. So how many kilometers per hour is the river speed?
6. Transport the poles from the material site on the expressway to the side of the expressway 500 meters away, and plant one at the roadside every 50 meters. It is also known that only three poles can be transported at a time, and 20 poles should be transported back to the material site. How to make reasonable arrangements to minimize the total journey of transport trucks? What's the minimum?
7. Master Wang wants to process a batch of parts. If 12 parts are processed per hour, it will take less time than planned 1/9. If 16 pieces are processed less per hour, it will take 3/5 hours more than before. How many parts are there in this batch?
8. Party A and Party B each process a certain number of parts. If A processes 24 pieces per hour and B processes 12 pieces per hour, then after B completes the task, A has 22 pieces left; If A processes 12 pieces per hour and B processes 24 pieces per hour, then after B completes the task, A still has 130 pieces left. How many parts will Party A and Party B process?
9. Two road repair teams, Team A and Team B, are fellow initiates on the 3,600-meter-long railway. When A has completed 3/4 of the assigned task and B has completed 4/5 and 40 meters of the assigned task, there are still 780 meters of tasks unfinished. How many meters did Team A and Team B get respectively?
The sixth grade math application problem (2) 1. Two cars, A and B, leave from A and B at the same time, meet in four hours, and then continue driving for three hours. At this time, the distance between A and B is10km, and the distance between B and A is 80km. How many hours does it take for bus A to arrive at location B?
2. Two rectangular pools A and B are filled with water, and the heights of the two pools are equal. It is known that the drain pipe of Pool A/KLOC-0 can drain water in 0/0 minute, and the drain pipe of Pool B can drain water in 6 minutes. How long does it take to open the drain pipes of pool A and pool B at the same time? The water level of pool A is exactly three times that of pool B?
3. When a car travels from A to B, the flat road accounts for 3/5 of the whole journey, 3/8 of the rest is uphill and the rest is downhill. When I came back, the uphill road was kilometers. How many kilometers is it between A and B?
4. It takes 4 hours for Party A and Party B to cooperate in a job, and 5 hours for Party B and Party C to cooperate. Now Party A, Party B and Party C will cooperate for two hours, and the rest will take six hours to complete. How many hours does Party B need to do this work alone?
A sporting goods store bought a batch of basketball, which was divided into first-class and second-class. The second best product is 20% cheaper than the first one. According to the principle of high quality and good price, the first-class product is priced at 20% profit, and the second-class product is priced at 15% profit. First-class basketball is more expensive than second-class basketball 14 yuan. What is the purchase price of a top basketball?
6. When a commodity is sold at a fixed price, everything can make a profit, 50 yuan. If 10 is sold at 80% price, which is equivalent to reducing the profit of selling 12 in 30 yuan, what is the price of each piece of this commodity?
7. Ride a motorcycle to catch a train from home to the railway station. 30 kilometers per hour, arrive 15 minutes earlier; If you drive at 20 kilometers per hour, you will be five minutes late. If you plan to arrive five minutes early, what should be the speed of the motorcycle?
8. There are two alloys, A and B, with different copper contents. A weighs 6 kg and B weighs 4 kg. Now, cut equal parts from alloy A and alloy B, respectively. The cut part of block A and the rest of block B are melted together, and then the cut part of block B and the rest of block A are melted together to obtain two new alloys with the same copper content. What is the weight of the part cut from each piece?
9. The price of a commodity at 1 1 per 5 yuan profit is as much as that at11per 0 yuan profit. What is the cost of this commodity?
10. Mr. Zhang ordered 80 pieces of a certain commodity from the store, and the price of each piece was 100 yuan. Mr. Zhang said to the store manager, "If you are willing to reduce the price by 1 yuan, I will order another 4 pieces." The store manager calculated that if the price is reduced by 5%, Mr. Zhang Can can still get as much profit as before, because his order quantity has increased. What is the cost of this commodity?
The sixth grade mathematics application problem (3) 1. A, B, C and D are 16, 12, 1 1 and 9 years old respectively. How many years ago, A and B were twice as old as C and D?
2. At both ends of a circular runway with a diameter of 200 meters, Party A and Party B respectively set off in the same direction at a riding speed of 6 meters per second and 5 meters per second, and run along the runway. 16 minutes How many times did A chase B?
3. There are 10 stations in the middle of a bus line. There are two kinds of trains: express and local. The speed of the express train is 1 of the local train. More than twice as much. The local train stops at every stop, and the express train only stops at one stop, with a stop time of 3 minutes. When the local train leaves 40 minutes later, the express train leaves from the same starting station, and both trains arrive at the finish line at the same time. How long does the express train take from the start to the end?
4. There are five piles of apples, the average of the smaller three piles of apples is 18, and the difference between the larger two piles is 5. There are an average of 26 apples in the larger 3 piles, and the difference between the smaller 2 piles is 7. There are an average of 22 apples in the largest and smallest piles. How many apples are there in each pile?
5. Class A, Class B and Class C donated books to Project Hope. It is known that one person in Class A donated 6 copies, two people donated 7 copies each, and the rest donated 1 1; One person in Class B donated 6 copies, three people donated 8 copies each, and the rest donated 1 1 copy; In Class C, two people donated four copies each, six people donated seven copies each, and the rest donated nine copies each. It is known that the total number of books donated by Class A is 28 more than that of Class B, and Class B is more than Class C 10 1 book ... The total number of books donated by each class is between 400 and 550. How many people are there in each class?
6. A company's color TV sets are sold at the original price, and each set makes a profit in 60 yuan; Now the price has been reduced, and as a result, the sales of color TV sets have increased by 1 times, and the total profit obtained has increased by 0. 5 times, how much is the price reduction of each color TV?
7. A project can be completed by team A alone 12 days, and team A can complete half of it in 3 days. Now, after a few days of cooperation between Team A and Team B, Team B completed it alone and found that the two time periods were equal. How many days will it take?
8. Two cups were filled with 40% and 10% saline respectively, and the concentration of mixed saline was 30% after being poured together. If 300 grams of 20% physiological saline is added, the concentration will become 25%. So how many grams is the original 40% saline?
9. two cars, a and b, start from a and b respectively, and the directions are opposite. At the time of departure, the speed ratio of A and B is 5: 4. After meeting, the speed of A decreases by 20% and the speed of B increases by 20%. Then when A arrives at B, B is still 10 km away from A, so how many kilometers are A and B apart?
10. Xiao Li and Xiao Zhang start to make the same kind of parts at the same time, and each person can make 1 part per minute, but Xiao Li has to rest every three parts 1 minute and Xiao Zhang has to rest every four parts 1 minute. Five minutes. Now they will finish the task of manufacturing 300 parts together. How many minutes will it take?
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