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It takes 56 seconds for a train to pass a 240 meter bridge, and 48 seconds for a train to pass a 144 meter tunnel at the same speed There are detailed formulas
Speed (240-144) / (56-48)
=96÷8
=12 m / S
Length 12 × 56-240
=672-240
=432m
It takes four minutes for a train to pass through a 240 meter cave and two minutes and 30 seconds to pass a 1080 meter bridge
Hello
4 minutes = 240 seconds
2 minutes 30 seconds = 150 seconds
speed
（1080-240）÷(240-150)
=840÷90
=28 / 3 M / S
Length 28 / 3x150-240 = 1400-240 = 1160m
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It takes 1.7 minutes for a train to cross a 2400 meter tunnel, and 48 minutes to cross a 1050 meter long bridge at the same speed
1.7 minutes = 102 seconds
Train speed (2400-1050) △ 102-48) = 1350 △ 54 = 25m / S
Train length 48x25-1050 = 1200-1050 = 150m
Give 20 practical questions to the fifth grade students (with answers)
1. A train passes the Nanjing Yangtze River Bridge. The bridge is 6700 meters long. The train is 140 meters long. The train runs 400 meters per minute. How many minutes does it take for the train to pass the Yangtze River Bridge?
According to the quantity relation, we know that if we want to find the passage time, we need to know the distance and speed. The distance is the length of the bridge plus the length of the train. The speed of the train is the known condition
Total distance: (m)
Passage time: (minutes)
A: it takes 17.1 minutes for this train to cross the Yangtze River Bridge
2. A train is 200 meters long. It takes 30 seconds for the whole train to pass the 700 meter long bridge. How many meters does this train travel per second?
We know that if we want to find the speed, we need to know the distance and the passing time. We can use the known condition of the bridge length and the vehicle length to find the distance, and the passing time is also known, so the speed can be easily found
Total distance: (m)
Train speed: (m)
A: the train travels 30 meters per second
3. A train is 240 meters long. The train travels 15 meters per second. It takes 20 seconds from the time when the train enters the cave to the time when the whole train leaves the cave. How long is the cave?
The analysis is the same as the train passing through the cave and bridge. The locomotive entering the cave is equivalent to the locomotive going on the bridge; the whole train leaving the cave is equivalent to the train leaving the bridge at the end of the car. In this problem, finding the length of the cave is equivalent to finding the length of the bridge. We must know the total distance and the length of the train. The length of the train is the known condition, so we need to use the speed and passing time given in the problem to find the total distance
Total distance:
Cave length: (m)
A: the cave is 60 meters long
The problem of sum times
1. The age of Qin Fen and his mother is 40 years old. His mother's age is four times that of Qin Fen. How old are Qin Fen and his mother?
We take Qin Fen's age as one time, "his mother's age is four times Qin Fen's", so the sum of Qin Fen's and his mother's age is equal to five times Qin Fen's age, which is 40 years old, that is (4 + 1) times, which can also be understood as five is 40 years old, so how much is one time, and then how much is four times?
(1) The multiple sum of Qin Fen and his mother's age is: 4 + 1 = 5 (multiple)
(2) Qin Fen's age: 40 △ 5 = 8 years old
(3) Mother's age: 8 × 4 = 32 years old
Comprehensive: 40 ÷ (4 + 1) = 8 years old, 8 × 4 = 32 years old
In order to ensure the correctness of this question, verify
(1) 8 + 32 = 40 years old (2) 32 △ 8 = 4 (Times)
The result of calculation meets the condition, so the solution is correct
2. A and B planes fly from the airport to the opposite direction at the same time. They fly 3600 km in three hours. A's speed is twice that of B. what's their speed?
Given that two airplanes fly 3600 km in three hours, we can calculate the flight range of two airplanes per hour, that is, the speed sum of the two airplanes. As can be seen from the figure, this speed sum is equivalent to three times the speed of airplane B. in this way, we can calculate the speed of airplane B, and then calculate the speed of airplane a according to the speed of airplane B
The speed of a and B aircraft is 800 km and 400 km per hour respectively
3. The younger brother has 20 extra-curricular books, and the elder brother has 25 extra-curricular books?
Thinking: (1) what is the constant quantity in the title before and after the elder brother gives the younger brother extra-curricular books?
(2) How many extra-curricular books do you need to know if you want to ask your brother to give him?
(3) If the remaining extra-curricular books of the elder brother are regarded as one time, how many times can the younger brother's extra-curricular books be regarded as the remaining extra-curricular books of the elder brother?
On the basis of thinking about the above questions, we can find out how many extra-curricular books the elder brother should give to the younger brother. According to the conditions, we need to find out how many extra-curricular books the elder brother has left. If we take the remaining extra-curricular books of the elder brother as one time, then the younger brother's extra-curricular books can be regarded as two times of the remaining extra-curricular books of the elder brother, that is, the common multiple of the two brothers is equivalent to three times of the remaining extra-curricular books of the elder brother, The total number of extra-curricular books of the two brothers is always the same
(1) The number of extracurricular books shared by the two brothers is 20 + 25 = 45
(2) After the elder brother gave his younger brother some extra-curricular books, the common multiple of the two brothers was 2 + 1 = 3
(3) The number of extra-curricular books left by my brother is 45 △ 3 = 15
(4) The number of extra-curricular books given by my brother to my brother is 25-15 = 10
Try to make a comprehensive formula:
4. The two grain depots of a and B used to have 170 tons of grain together. Later, 30 tons of grain were transported out of a and 10 tons were transported in to B. at this time, the grain in a's stock was twice that in B's stock. How many tons of grain were stored in each of the two grain depots?
According to the fact that 170 tons of grain existed in the two warehouses, 30 tons were transported out of warehouse A and 10 tons were brought in to warehouse B, we can find out how many tons of grain existed in warehouse A and warehouse B. according to "at this time, the grain in warehouse A is twice that in warehouse B", if we take the grain in warehouse B as one time, then the grain in warehouse A and warehouse B is three times that in warehouse B, Then we can find out how many tons of grain were stored in warehouse B. finally, we can find out how many tons of grain were stored in warehouse a
There are 130 tons of grain in a warehouse and 40 tons in B warehouse
[example 1] there are 13 students in a group, and at least two of them have their birthdays in the same month. Why?
[analysis] there are 12 months in a year, and everyone's birthday must be in one of them. If we regard these 12 months as 12 "drawers", 13 students' birthdays as 13 "apples", and put 13 apples into 12 drawers, there must be at least 2 apples in one drawer, that is to say, at least 2 students have their birthdays in the same month
[example 2] for any four natural numbers, the difference between at least two of them is a multiple of 3. Why?
[analysis and solution] first of all, we need to make clear such a rule: if the remainder of two natural numbers divided by 3 is the same, then the difference between the two natural numbers is a multiple of 3. The remainder of any natural number divided by 3 is either 0, or 1, or 2. According to these three cases, natural numbers can be divided into three categories, These three types are the three "drawers" we want to make. We regard four numbers as "apples". According to the principle of drawers, there must be at least two numbers in a drawer. In other words, four natural numbers are divided into three categories, and at least two of them are of the same category. Since they are of the same category, the remainder of the two numbers divided by three must be the same, The difference between at least two natural numbers is a multiple of three
[example 3] there are 15 socks in each of the five colors with the same specifications and sizes in the box. No matter how many socks are taken out of the box, how many socks can guarantee three pairs of socks (no left or right socks)?
If you take 6 or 9 socks out of the box, can you make 3 pairs of socks? The answer is No
Five drawers are made according to five colors. According to drawer principle 1, as long as six socks are taken out, there will always be two in one drawer, and the two can be matched into one pair. If you take away this pair, there are still four left. If you add another two, you can make another six. According to drawer principle 1, you can make another pair. If you add another two, you can get the third pair. Therefore, if you take at least 6 + 2 + 2 = 10 socks, you will make three pairs
Thinking: 1. Can we use drawer principle 2 to get the result directly?
2. Change the requirement in the question to 3 pairs of socks of different colors. How many socks should be taken out at least?
3. How about changing the requirement in the question to 3 pairs of socks of the same color?
[example 4] there are 35 wooden balls of the same size in a cloth bag, including 10 white, 10 yellow and 10 red balls, 3 blue balls and 2 green balls?
[analysis and solution] start with the most unfavorable situation
The most disadvantageous situation is that three of the five balls are blue and two are green
Next, white, yellow and red are regarded as three drawers. Because there are more than four balls of these three colors, according to drawer principle 2, as long as the number of balls taken out is more than (4-1) × 3 = 9, that is, at least 10 balls should be taken out, at least four balls can be taken out of the same drawer (the same color)
Therefore, at least 10 + 5 = 15 balls should be taken out to meet the requirements
Thinking: change the requirements to four different colors, or two of the same color, what's the situation?
When we come across the problem of "judging whether there are at least a few properties of a certain thing", we think of it drawer principle, which is your "decisive" way
There are 100 chickens and rabbits in total. The number of legs of chicken is 28 less than that of rabbit. How many are there in chicken and rabbit?
6、 Drawer principle, parity problem
1. A cloth bag contains gloves of the same size but different colors. There are four kinds of colors: black, red, blue and yellow. How many gloves do you need to feel at least to ensure that there are three pairs of gloves of the same color?
2. There are several building blocks of four colors. Each person can take 1-2 pieces at will. At least a few people can take them to ensure that there are 50 balls in a box, of which 10 are red, 10 are green, 10 are yellow, 10 are blue, and the rest are white balls and black balls. In order to ensure that the balls taken out contain at least 7 balls of the same color, how many balls must be taken out of the bag at least?
It is known that a, B and C can plant 24, 30 and 32 trees each day. A plants trees in a and C plants trees in B. B first plants trees in a and then transfers to B. the two plots begin to bundle at the same time. How many days should b transfer from a to B?
2. There are three grasslands with an area of 5 mu, 15 mu and 24 Mu respectively. The grass on the grassland is as thick and grows as fast. The first grassland can feed 10 cows for 30 days, and the second grassland can feed 28 cows for 45 days. How many cows can the third grassland feed for 80 days?
3. For a project, if it is contracted by team a and team B and can be completed in 2.4 days, it needs to pay 1800 yuan; if it is contracted by team B and team C and can be completed in 3 + 3 / 4 days, it needs to pay 1500 yuan; if it is contracted by team a and team C and can be completed in 2 + 6 / 7 days, it needs to pay 1600 yuan?
When a cuboid container is filled with water for 3 minutes, the bottom area of the cuboid container is 18 cm higher than that of the known one
5. Party A and Party B
RELATED INFORMATIONS
- 1. It takes six seconds for a train to pass by a power pole on the side of the road. It takes 46 seconds for a train to cross a 2000 meter long bridge at the same speed. How long is the train
- 2. It took 24 seconds for a train to pass through the first tunnel with a length of 360 meters, and then it took 16 seconds to pass through the second tunnel with a length of 216 meters. This train is facing another train with a length of 75 meters and a speed of 86.4 kilometers per hour. What is the time for the wrong train to cross?
- 3. A train passes through two tunnels at the same speed. The first 420 meters takes 27 seconds, and the second 480 meters takes 30 seconds?
- 4. Grade 5 math problem: a train passes through two tunnels at the same speed. One tunnel is 420 meters long and runs for 27 seconds. The other tunnel is 480 meters long and runs for 30 seconds How long is the train
- 5. A 240 meter long train passes through an 881 meter long tunnel at a speed of 1500 meters per minute. How many minutes does it take from the front of the train to the rear of the train to leave the tunnel?
- 6. A train passes through a 450 meter long tunnel at a speed of 18 meters per second. It takes 35 seconds from the front of the train entering the tunnel to the rear of the train leaving the tunnel to calculate the length of the train
- 7. A train through the tunnel, from the front into the tunnel to the rear out of the tunnel takes 1 minute and 30 seconds, the known speed of the train is 100 km
- 8. It takes 50 seconds for a 1000m bridge and 70 seconds for a 1500m bridge. If the speed of the train is reduced by 20%, how much does it take for the train to pass through the 1950m long tunnel [solve with the equation of one variable and one degree]
- 9. It takes 24 seconds for the first 360 meter tunnel and 16 seconds for the second 220 meter tunnel
- 10. A train runs 18 kilometers per second, this train runs 1 minute 33 seconds, the whole train passes a 1498 meter long bridge, how long is this train?
- 11. When a train enters a 300m long tunnel, it takes 20s from entering the tunnel to leaving completely. The time for the train to be completely in the tunnel is 10s
- 12. It takes 20s for a train to pass through a 300m tunnel. The tunnel light shines on the train for 10s. Ask the conductor
- 13. A train runs at a speed of 72km / h, and there is a tunnel directly in front of it. The train must whistle before entering the tunnel. The driver hears the echo reflected from the cliff at the tunnel entrance after 1.5s. How far is the driver from the tunnel when he hears the echo? (sound speed is 340m / s)
- 14. Wang Xiaoya was riding on a 200m long train with a speed of 72km / h. from the window, she could see the train running head-on Wang Xiaoya was riding on a 200m long train running at a constant speed of 72km / h. from the window, she saw a 300m long freight train coming in front of her. The passing time was 10s, so she calculated the speed of the freight train
- 15. A train is 200 meters long and has to pass through a 300 meter long tunnel. How many meters does the train travel from the front to the rear of the train?
- 16. A train runs at a constant speed through a 500m long tunnel, If it takes 30 seconds for the train to enter the tunnel and leave the tunnel completely, and the time for the whole train to be in the tunnel is 20 seconds, the length of the train can be calculated Using equation
- 17. It took 50 seconds for a train to pass through a 1140 meter long bridge (from the front of the train to the rear of the train leaving the bridge), and 80 seconds for the train to pass through a 1980 meter long tunnel?
- 18. A certain section of railway is made up of L-length rails one by one. When a train is moving at a constant speed, a passenger in the train needs to measure the speed of the train. He has measured that the time interval of N consecutive vibrations when the train passes through the rail joint is t, then the relationship V of the speed V is calculated=
- 19. On the double track railway, there are two fast and slow trains, both 250m long, running in the same direction at the speed of 50km / h and 45km / h respectively How much time do they overtake? Use the system of linear equations with one variable to solve!
- 20. A freight car is running on the straight road at the speed of V1 = 28.8km/h. Due to the wrong scheduling, a passenger car behind it is driving on the same road at the speed of V2 = 72km / h. at the distance of S0 = 600m, the driver of the passenger car immediately stops the truck. In order to avoid collision, at least how much speed should the passenger car speed up?