Answer: 28 minutes
Analysis: Assuming that the total running time is S, Party A and Party B walk AB together for the first time, S+AB for the second time, 8 minutes for the first time, and 6+ 10= 16 minutes for the second time, then the time for them to walk AB together is half of the whole S time, according to the speed and calculation.
Xiaoming and Xiaoying go back and forth to A and B respectively on the expressway. Let's assume that at the beginning, they went in opposite directions. If they meet for the first time at a distance of 3 kilometers and meet for the second time at a distance of 2 kilometers, what is the distance between A and B?
Answer: 7 kilometers
Analysis: Xiao Ming met for the first time and walked 3 kilometers. When we met for the second time, Xiao Ming walked 3 kilometers, met 9 kilometers, and subtracted 2, it was 7 kilometers. This kind of problem has a formula (2N- 1)=M (where n is the number of encounters and m is the total length of two people * * *).
3. Party A and Party B run towards each other around the circular track at a uniform speed, starting at both ends of the circular diameter. If they start at the same time, they will meet for the first time when Party A runs 60 meters, and when Party B is still 80 meters short.
When they met for the second time, they asked about the length of the runway.
Answer: 200 meters
Analysis shows that Party A and Party B ran for one and a half laps when they met for the second time. At this time, Party A ran 60*3= 180 meters, and the total length was reduced by 80 meters, so 1.5S=S-80+ 180 got the total length S equal to 200 meters.
4. two cars, a and b, start from a and b respectively at the same time and walk in opposite directions. Car A travels 45 kilometers per hour, while car B travels 36 dry meters per hour. After meeting, they continued to advance at the original speed and arrived separately.
Return immediately after arriving at the destination, so continue to drive back and forth. It is known that the distance between the second venue and the third venue on the way is 40 kilometers. How far is it between a and b?
Answer: 90 kilometers
Analysis: As shown in the figure, with the line segment diagram method, we can know that V A: V B =5:4 from the known conditions, so at the same time, S A: S B =V A: V B =5:4, and from the formula (2N- 1)=M, we can know that the distance between the second meeting and the third meeting point is 4/9 of the total length.
Party A and Party B run back and forth on a straight road 90 meters apart. Party A's speed is 3 meters per second, and Party B's speed is 2 meters per second. If they start from both ends of the straight road at the same time, how many times do they meet in 10 minutes?
Answer: 17 times
Analysis: According to the formula (2N- 1)=M, it is 90÷(2+3)= 18S (the time of first meeting), and then each meeting takes 36 seconds, (600-18) ÷ 36 = 66.
6. The express train and the local train travel in opposite directions. The length of the express train is 50 meters, the length of the local train is 80 meters, and the speed of the express train is twice that of the local train. If it takes five seconds for a person sitting in the local train to see the express train passing through the window, how long does it take for a person sitting in the local train to see the local train passing through the window?
Answer: 8 seconds
Analysis: When the local train sees the express train passing through the window, the distance is 50 meters long and it takes 5 seconds, so the sum of the speeds of the local train and the express train is 50÷5= 10 m/s, while when the express train sees the local train passing through the window, the distance is 80 meters long and the sum of the speeds is still 10 m/s, so the time is 80 ÷.
7. Xiaogang and Xiao Qiang rented a boat, rowed upstream and accidentally dropped the kettle into the river. When they found and adjusted the bow, the kettle was 2 kilometers away from the ship. Assuming that the speed of the ship was 4 kilometers per hour at that time and now it is 2 kilometers per hour, how long will it take them to catch up with the kettle?
Answer: 0.5 hours
Analysis: For a typical running boat problem, when the boat turns around to chase the kettle, the speed difference between them is 2+4-2 = 4km/ hour, and the chasing distance is 2km, so the chasing time = distance difference ÷ speed difference = 2 ÷ 4 = 0.5h ..
8. Party A and Party B train on the elliptical track and run in reverse from the same place at the same time. After the first lap, everyone returned to the starting point and immediately turned back to speed up the second lap. When running the first lap, Party B's speed is the speed of Party A..
2/3 of the degree, the speed of A in the second lap is higher than that of the first lap 1/3, and the speed of B in the second lap is higher than that of the first lap 1/5. It is known that the second intersection of A and B is 90 meters away from the first intersection/kloc-0.
How long is this oval runway?
Answer: 400 meters
Analysis: As shown in the figure below, point A is the starting point. Because the speed of the first lap B is 2/3 of that of A, the distance from point B to A for the first time is 3/5 of the whole journey. When A finishes a lap and reaches point A, point C is 1/3, at which time A accelerates 1/3, and the speed ratio of A and B becomes 2. The distance between them is 65438+ 0/3 of the whole journey. At this time, B accelerates 1/5, and the speed ratio between Party A and Party B becomes 4: 12/5=5:3. At this time, it becomes an encounter problem with a distance of 1/3. When Party A and Party B meet for the second time, Party B takes 1/3 of the total length. Therefore, the distance BD between two intersections is 3/5- 1/8= 19/40 of the total length, so the total length of the elliptical runway is 190÷ 19/40=400 meters.
9. The express train and the local train leave from A and B at the same time, in opposite directions, and meet after 5 hours. It is known that it takes 12.5 hours for the local train to travel from B to A, and it will return after stopping in A for 0.5 hours. The express train stops at b 1 hour and then returns. So how long does it take for two trains to meet from the first time to the second time?
Answer: 54/5 hours
Analysis: Because the meeting time between the slow train and the slow train is 5 hours, it takes 12.5-5=7.5 hours for the slow train to reach A, and the journey of the slow train of 7.5 hours is just equal to the journey of the express train of 5 hours. Because the distance is constant and time is proportional to speed, V is fast: V is slow =t is slow: T is fast = 7.5: 5 = 3.2.
10. On the 400m circuit, the distance between point A and point B is100m. Two people, a and b, start from point a and point b at the same time and run counterclockwise. A is 5 meters per second and B is 4 meters per second. Everyone runs.
100 meters, it takes 10 seconds to stop. So, how many seconds does it take for A to catch up with B?
Answer: 140 seconds
Analysis: 100÷(5-4)= 100 second, 100*5=500, a * * * takes four breaks, so it needs100+4 */kloc-0.
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