Mathematical Olympiad of Grade Five in Primary School
1. A 50-meter-long train took 25 seconds to pass through a 200-meter-long cave. How many meters does this train travel per second? A 240-meter-long train crosses a bridge at a speed of 30 meters per second. It takes 1 minute to get on the bridge at the front and get off the bridge at the back. How long is this bridge?
3. A truck is 240 meters long and runs at the speed of 15 meters per second. The whole train keeps going through tunnels and bridges. It takes 40 seconds, and the bridge length is150m. How long is this tunnel?
4. It takes 75 seconds for a train to cross a bridge 1200m long, and only 15s for a train to cross a roadside pole at the same speed. How long is the train?
On the ascending and descending tracks, two trains face each other. One train is182m long and runs at the speed of18m per second, while the other train runs at the speed of17m per second. Time taken for two trains to cross the train by mistake 10 second. How long is the other train?
6.A car travels 6 kilometers per hour, and B car travels 5 kilometers per hour. The two cars walked back to each other at the same time at a distance of 10 km. A few hours later, they were 65 kilometers apart.
7. Party A travels 9 kilometers per hour and Party B travels 7 kilometers per hour. Party A travels south from Nanzhuang and Party B travels north from Beizhuang. Three hours later, they were 60 kilometers apart. How many kilometers are the two villages apart?
8. The distance between east and west towns is 20 kilometers. Party A and Party B set out from two towns at the same time and went in opposite directions. The distance of Party A per hour is twice that of Party B, and after 3 hours, the distance between them is 56 kilometers. What is everyone's speed?
9. The students of Team A and Team B started from two places 18km apart and walked in opposite directions at the same time. A classmate keeps cycling back and forth between the two teams at the speed of 15 km per hour. Team A travels 5 kilometers per hour, while Team B travels 4 kilometers per hour. How many kilometers did the cyclist walk when the two teams met?
10, A and B are 400 kilometers apart. Two cars, A and B, leave from two places at the same time. Car A travels 38 kilometers per hour and car B travels 42 kilometers per hour. A swallow flies to car B at the same time with car A at a speed of 50 kilometers per hour. When it meets car B, it turns back to car A. How many kilometers did the swallow fly before the two cars met?
Fifth grade olympiad in the second primary school
1, Party A, Party B and Party C plant trees in plots A and B, with 900 trees in plot A and 250 trees in plot B/kloc-0 ... It is known that Party A, Party B and Party C can plant 24, 30 and 32 trees each day. Party A plants trees in Site A, Party C plants trees in Site B, Party B plants trees in Site A first, and then goes to Site B ... The two plots start and end at the same time. On what day should B be transferred from A to B? 2. There are three grasslands with an area of 5 15 and 24 mu respectively. The grass on the grass is as thick and grows as fast. The first meadow can feed 10 cows for 30 days, the second meadow can feed 28 cows for 45 days, and how many cows can the third meadow feed for 80 days?
3. A project is contracted by Party A and Party B, which can be completed in 2.4 days and needs to be paid 1800 yuan; Contracted by Team B and Team C, it can be completed in 3+3/4 days, and it needs to be paid 1500 yuan; 2+6/7 days, cost 1600 yuan. On the premise of ensuring the completion within one week, which team should be selected for the lowest cost?
A rectangular iron block is placed in a cylindrical container. Now turn on the tap and pour the water into the container. In 3 minutes, the water just passed the top of the cuboid. In another 18 minutes, the water has filled the container. It is known that the height of a container is 50 cm and the height of a cuboid is 20 cm. Find the ratio of the bottom area of a cuboid to the bottom area of a container.
5. Two bosses of Party A and Party B buy a fashion at the same price, and Party B buys 1/5 sets more than Party A, and then Party A and Party B sell them at profit margins of 80% and 50% respectively. After both of them were sold out, A still made more profits than B, just enough for him to buy 10 this fashion. How many sets of this fashion A did you buy?
6. There are two water pipes A and B, and water is injected into two pools with the same size at the same time. At the same time, the water injection ratio of A and B is 7: 5. After 2+ 1/3 hours, the sum of the water injected into A and B is exactly one pool. At this time, the water injection rate of pipe A is increased by 25%, while the water injection rate of pipe B is unchanged. So, how many hours does it take for pipeline A to fill pool A and pipeline B to fill pool B?
Xiao Ming walks from home to school in the morning. When he ran halfway, his father found that Xiao Ming's math book was left at home, and then he rode to deliver it to Xiao Ming. When catching up, Xiao Ming still had 3/ 10. Before the distance was over, Xiao Ming got on his father's car and was sent to school by his father, so Xiao Ming arrived at school five minutes earlier than walking alone. How long does it take Xiaoming to walk from home to school?
8. Both A and B start from place A and pass through place B to place C. The distance between A and B is equal to the distance between B and C. The speed of B is 80% of that of A. It is known that B started earlier than A 1 1 minute, but stayed at place B for 7 minutes, while A kept driving to place C. Finally, B train was better than A train. Then car A will overtake car B a few minutes after car B leaves.
9. Party A and Party B have two cleaning vehicles to clean the road between things. It takes 15 hours for car A to clean alone, and 15 hours for car B to clean alone. Two cars leave from East and West at the same time. When they met, car A cleaned more than car B 12 kilometers. How many kilometers is there between East and West?
At present, there are 4 containers weighing 3 tons, 5 containers weighing 2.5 tons, 14 containers weighing 1.5 tons, and 7 containers weighing 1 ton. So how many cars with a load of 4.5 tons are needed to transport these containers at one time?
Mathematical Olympiad in Grade Three and Grade Five of Primary School
1. Two athletes are practicing long-distance running on the ring road around the lake. A runs 250 meters per minute, and B runs 200 meters per minute. They both set out for the same place and direction at the same time. After 45 minutes, A catches up with B. If they start in opposite directions at the same time, how many minutes will it take them to meet? A group of cyclists rode from A to B at a speed of 24 kilometers per hour. Two hours later, a motorcycle also rode from A to B at a speed of 56 kilometers per hour, and caught up with the cyclist at half the distance from A to B. Q: How many kilometers is there between A and B?
Xiao Ai and Xiao Qing walked out of two cities, A and B, face to face. They meet at a distance of 35km from a certain city, return at the same speed along the original road immediately after arriving at the other city, and meet at a distance of 0/5km from a certain city/kloc-. How many kilometers are the two cities apart?
4. Three cars, A, B and C, leave from A to B at the same time. The speeds of A and B are 50 kilometers and 38 kilometers per hour respectively. An oncoming truck met them 4 hours, 5 hours and 6 hours after their departure from A, B and C respectively. Find the speed of car C.
The distance between Party A and Party B is 258km. A car and a tractor drove out of two places at the same time and met four hours later. As we all know, the speed of a car is twice that of a tractor. How many kilometers did the car travel more than the tractor when they met?
6. Two cars, A and B, set off from two stations at the same time and walked in opposite directions. When they first met, they were 28 kilometers away from Station A. After meeting, the two cars moved on. After arriving at the two stops, immediately return along the original road. The second meeting is 60 kilometers away from Station A. What is the distance between Station A and bilibili?
7. Xiao Zhang and Xiao Wang set out from Party A and Party B at 8: 00 a.m. and arrived at 10, with a distance of112.5km; Continue driving until 1 in the afternoon, and the distance between the two cars is still 1 12.5 km. How many kilometers are there between these two places?
8. The distance between the two places is 380 kilometers. There are two cars leaving from two places at the same time. Originally, car A planned to run at 36 kilometers per hour and car B planned to run at 40 kilometers per hour, but when driving, car A changed speed and left at 40 kilometers per hour. How many kilometers did B car travel less than originally planned when they met?
9. The distance between east and west towns is 240 kilometers. A bus goes from Dongzhen to Xizhen at 8 am, and a truck goes from Xizhen to Dongzhen at 9 am. At noon, the two cars met at the midpoint of the two towns. If both cars leave at 8: 00 a.m. with the same speed, how many kilometers are the two cars apart by morning 10?
10. The bus and truck leave from two stations at the same time. Buses travel 54 kilometers per hour and trucks travel 48 kilometers per hour. After the two cars met, they continued to drive at the original speed. The bus returns immediately after arriving at the second stop, and the truck returns immediately after arriving at the first stop. When the two cars meet again, the bus travels 2 16 kilometers more than the truck. How many kilometers is the distance between the two stops?