Uncle Wang has a watch. He found that the watch was 30 seconds faster than the alarm clock at home, but the alarm clock was 30 seconds slower than the standard time. So how many seconds is the time difference between day and night of Uncle Wang's watch?
If the analytical alarm clock is slower than the standard one, then it only runs (3600-30)÷3600 hours and the watch is faster than the alarm clock, then it runs (3600+30)/3600 hours and then the standard time runs 1 hour and the watch runs (3600-30) ÷. Then the watch is1-(3600-30) ÷ 3600x (3600+30) ÷ 3600 =1-14399 ÷14400 = 65440.
Xiao Qiang's home has an alarm clock, which is 3 o'clock faster than the standard time every hour. One night 10, Xiao Qiang aimed at the alarm clock. He wants to get up at 6 o'clock the next morning. What time should he set the alarm clock?
Analysis 6: 24
Consolidating Xiaoxiang's home has an alarm clock, which is 3 minutes slower than the standard time every hour. At half past eight one night, Xiaoxiang aimed at the alarm clock. He wanted to get up at 6: 30 the next morning, so he set the alarm clock at 6: 30. When does this alarm clock ring?
Analyze 7 points
When the clock indicates 1: 45, what is the obtuse angle between the hour hand and the minute hand?
142.5 degree analysis
Example 2 Now the clock shows 10 hour. Then, how many minutes later, the minute hand and the hour hand coincide for the first time; How many minutes later, the minute hand and the hour hand coincide for the second time?
The analytical minute hand walks 12 grid per hour, the hour hand walks 1 grid, and the minute hand walks more than the hour hand12-1=1grid, and walks more every minute1/kloc-. At 10, the hour hand and the minute hand are separated by 10, which is the first overlap. The minute hand moves 10 more than the hour hand, and the time it takes is10 ÷11/60 = 54 6/60.
At 4: 00, how many minutes did the hour hand and minute hand of the combined clock first coincide?
The analysis of this problem is a catch-up problem. The catching-up distance is 20 squares and the speed difference is 12/60- 1/60, so the catching-up time is 20/( 12/60- 1/60) (minutes).
It can also be calculated in degrees: 4*30/5.5=240/ 1 1 min.
It's 3 o'clock now. When did the hour hand and minute hand first coincide?
According to the meaning of the question, at 3 o'clock, the hour hand and the minute hand form 90 degrees, and the minute hand needs to chase 90 degrees for the first time.
When was the first time that the hour hand and minute hand of a clock were vertical at 8: 00?
Solving this problem is a catching-up problem, but the catching-up distance is 4 squares (from the original 40 squares to 15 squares) and the speed difference is 0, so the catching-up time is: (minutes).
After 2 o'clock, when does the minute hand and the hour hand first form a right angle?
According to the meaning of the question, at 2 o'clock, the hour hand and the minute hand form 60 degrees, and it takes 90 degrees to be vertical for the first time, that is, the minute hand chases 90+60= 150 (degrees), (minutes).
Between 8 o'clock and 9 o'clock, the hour hand and the minute hand are on both sides of "8", and the ray distance formed by the two hands and "8" is equal. What time is eight o'clock?
When analyzing 8 o'clock, the hour hand is 40 squares more clockwise than the minute hand. If the meaning of the question is satisfied, the hour hand goes through x squares, then the minute hand goes through 40-x squares, and then the hour hand and the minute hand * * * go through x+(40-x)=40 squares. So the required time is minutes, that is, 8 o'clock is the time required in the question.
It's 10. How long will it take for the hour hand and minute hand to line up for the first time?
The analytical hour hand speed is 360÷ 12÷60=0.5 (degrees/minutes), and the minute hand speed is 360÷60=6 (degrees/minutes), that is, the speed difference between the minute hand and the hour hand is 6-0.5=5.5 (degrees/minutes), 65433. , so the answer is (points)
At what time between 9 o'clock and 10, the minute hand and the hour hand are in a straight line?
According to the question, at 9 o'clock, the hour hand and the minute hand are 90 degrees. The first minute hand needs to chase 90 degrees in a straight line and the second minute hand needs to chase 270 degrees in a straight line. The answers are (minutes) and (minutes).
Just after 8 o'clock in the evening, Xiaohua soon began to do his homework. When he looks at the clock, the hour hand and the minute hand are in a straight line. Look at the clock after you finish your homework. It's not 9 o'clock yet, and the minute hand and the hour hand coincide. How long did it take Xiaohua to do his homework?
According to the meaning of the question, it takes 180 degrees to catch up with the other side in a straight line, (points)
Example 8 At 6 o'clock in the afternoon, someone went out to buy something. He looked at his watch and found that the angle between the hour hand and the minute hand of the watch was 1 10. When he got home before 7 o'clock, he found that the angle between the hour hand and the minute hand was still 1 10. So how many minutes did this man go out?
The schematic diagram is analyzed below. At first, the minute hand was at the position of 1 10 on the left side of the hour hand, and then it was at the position of 1 10 on the right side of the hour hand.
Then, the minute hand caught up with110+1/kloc-0 = 220, corresponding to the grid. It took a few minutes. So the man went out for 40 minutes.
Comments: Through the above example, we can see that sometimes the number of squares is divided, and sometimes the number of squares is divided, because sometimes the hour hand and the minute hand go together, which corresponds to the speed sum; Sometimes the minute hand catches up with the hour hand, and the corresponding speed is poor. For this question, you can also change the question to: "Go out at 9 o'clock and come back at 9 o'clock, the included angle is 1 10, and the answer is still 40 minutes."
At 9 o'clock in the morning, when the hour hand and minute hand of a clock coincide, what time does the clock indicate?
The first time that the hour hand and the minute hand overlap is: (minutes). When the hour and minute hands of the clock coincide, the clock indicates 9: 00.
Example 10 When Xiaohong started doing her homework at 8 o'clock in the morning, the hour hand and the minute hand coincided. When 10 minute ends, the hour hand and the minute hand coincide again. How long does it take Xiaohong to do her homework?
Analysis of more than 8 o'clock, the time when the hour hand and the minute hand overlap is: (minutes) 10, and the time when the hour hand and the minute hand overlap is: (minutes). Xiaohong takes the time to do her homework.
Example 1 1 Xiaohong began to solve a math problem between 9: 00 and 10: 00. At that time, the hour hand and the minute hand were in a straight line. Xiaohong solved the problem, and the hour hand and the minute hand coincided for the first time. How long did it take Xiaohong to solve this problem?
Between 9 o'clock and 10, the moment when the minute hand and the hour hand are in a straight line is: (minutes), and the moment when the hour hand and the minute hand first coincide is: (minutes), so the time spent on this question is: (minutes).
Example 12 When an animated film was shown at a price less than 1, Xiao Ming found that the positions of the hour hand and the minute hand on the watch at the end of the film were just exchanged with the positions at the beginning. How long did this cartoon show?
According to the meaning of the question, the hour hand just went to the minute hand position, and the minute hand just went to the hour hand position. They walked a circle, that is (minutes)
Example 13 now has a clock showing 10 hour. Then, how many minutes later, the minute hand and the hour hand coincide for the first time; How many minutes later, the minute hand and the hour hand coincide for the second time?
According to the meaning of the question, at 10, the hour hand and the minute hand are 60 degrees, and the minute hand needs to chase 360-60=300 degrees for the first time, and 360 degrees for the second time, that is, minutes.
Module 2, Time Standard and Alarm Clock Problem
Example 14 Zhong Min has an alarm clock, which is 2 minutes faster than the standard time every hour. At nine o'clock on Sunday morning, Zhong Min aimed at the alarm clock and set the bell. She wants the alarm clock to ring at 1 1: 30 to remind her to help her mother cook. What time should Zhong Min set the alarm clock?
The speed ratio between the alarm clock and the standard time is 62: 60 = 3 1: 30,1:50, and the difference between 0: 30 and 9: 00 according to the cross method is150× 3130.
Example 15 elephant has an alarm clock, which is 2 minutes slower than the standard time every hour. One night at 9 o'clock sharp, Xiaoxiang aimed at the alarm clock. He wanted to get up at 6: 40 the next morning, so he set the alarm clock at 6: 40. When does this alarm clock ring?
The speed ratio between the alarm clock and the standard time is 58:60=29:30, and there is a difference of 580 minutes between 9 pm and 6: 40 the next morning, that is, the standard time has passed 580×30÷29=600 minutes, so the standard time is 7 o'clock.
Example 16 has a clock that is 20 seconds fast per hour. March 1 Sunday noon 12 is accurate. When is the next exact time?
The speed difference between the analysis clock and the standard time is 20 seconds/hour, because the hands of the clock return to the starting position after 12 hours, so by the next accurate time, the clock has gone 12×3600÷20=2 160 (hour), which is 90 days, so the next time.
17 Xiaoming has two old wall clocks, one is 20 minutes fast and the other is 30 minutes slow every day. Now set these two old wall clocks to the standard time at the same time. How many days will it take them to display the standard time again at the same time?
The speed difference between the fast resolution wall clock and the standard time is 20 minutes/day, and the speed difference between the slow resolution wall clock and the standard time is 30 minutes/day. The fast resolution wall clock needs 12×60÷30=24 (days), and the slow resolution wall clock needs 12×60÷20=36 (days).
Example 18 A scientist designed a strange clock. Its day and night have 10 hour and each hour has 100 minute (as shown on the right). When this clock shows 5 o'clock, it is actually noon12; When this clock shows 6: 75, what time is it actually?
The standard clock is 24×60= 1440 (minutes), the odd clock is100×10 =1000 (minutes), and the odd clock passes 175 from 5: 00 to 6: 75. According to the crossover method,
Watches are 60 seconds faster than alarm clocks, and alarm clocks are 60 seconds slower than standard time. Set your watch at 8 o'clock sharp. What time does the watch say 12 exactly?
According to the meaning of the question, the alarm clock goes for 3600 seconds, the watch goes for 3660 seconds, and the alarm clock goes for 3540 seconds in one hour of standard time. So in the standard time of one hour, the watch runs 3660÷3600×3540 = 3599 (seconds), that is to say, the watch is slow 1 second per hour, so the time displayed by the watch at 12 is1:59.
Module 3
Someone has a watch and an alarm clock. The watch is 30 seconds slower than the alarm clock, which is 30 seconds faster than the standard time. Q: How many seconds is the time difference between this watch and the standard day and night?
According to the meaning of the question, after 60 minutes of standard time, the alarm clock goes for 60.5 minutes. According to the cross method, the alarm clock takes 60 minutes, the standard time takes 60×60÷60.5 minutes, and the watch takes 59.5 minutes. According to the cross method, the watch goes 59.5×24×60 \u( 60×
The temperature at Alpine weather station varies greatly during the day and at night. Because of the influence of temperature, the wall clock doesn't work normally. It is 30 seconds faster during the day and 20 seconds slower at night. If the wall clock is aimed at the early morning of 10, when is the earliest time when the wall clock is exactly 3 minutes fast?
According to the meaning of the question, a day and night is fast 10 second, (3×60-30)÷ 10= 15 (days), so first set the wall clock to15+1=/kloc.
The fast clock is 1 min faster than the standard time, and the slow clock is 3 minutes slower than the standard time. Adjust both clocks to the standard time at the same time. As a result, within 24 hours, the fast clock shows 9 o'clock sharp and the slow clock shows 8 o'clock sharp. What is the standard time at this time?
According to the meaning of the question, the standard time is 60 minutes, the fast time is 6 1 minute, and the slow time is 57 minutes, that is, every 60 minutes of the standard time, the fast time is 4 minutes longer than the slow time, and 60÷4= 15 (hours) is faster than the standard time 15 hours.
Example 23 Xiaoming has to go to school at 8 am, but the alarm clock at home stops at 6 am 10. He wound his watch but forgot to set it, so he hurried to school. When he got to school, he was 10 minutes early. At noon 12, after school, Xiao Ming went home to have a look, and it was only 1 1 exactly. If Xiaoming goes to school at the same time as he goes to school, how many minutes has his alarm clock stopped?
According to the meaning of the question, Xiaoming's time from school to school is 290 minutes (1 1 minus 6 points 10 points), and his time to go to school is 250 minutes (8 o'clock to 12 points, plus 10 points in advance), so he goes to school *