Mathematics problems and detailed explanations for the junior high school 15

Mickey Mouse 4000 25 = 160 minutes.

Donald Duck's time must be fixed, because no one interferes, so just calculate the time that Mickey Mouse has increased due to interference, and it is easy to make Mickey Mouse waste more than 200-160 = 40 minutes.

After analysis: every time Donald Duck presses, (nth time) the minute when Mickey Mouse first reverses must be wasted, and the regression distance is then n 10% 25 (m); To complete this regressive stretch of the road, you need to walk again (n 10% 25) 25=n 10% (minutes), so each time you press Mickey Mouse to complete the journey, the time to complete the journey increases by 1+n 10% (minutes).

1+1×10%）+1+2×10%）+1+3×10%）+1+n×10%）

n+（1+2+3+…+n)×10%

At this time, you need the summation formula of the equal difference series, I don't know if you have learned it, it is 1+2+3+....+n=n(n+1) 2,(If you don't know, you can search for the difference series, and I won't answer it here.) So:

Original = n+n(n+1) 20=n(n+21) 20 40

Since n is a positive integer, the inequality holds when solving the inequality to give n 20.

Some of the knowledge used in it may not have been learned yet, so you can continue to ask.

Solution: According to the topic, (This is also a matter of pursuit.) Idea: How many times is "at least" asked in the question. Then the less Donald Duck presses the remote, the better, that is, as long as you let Mickey Mouse not exceed himself. )

Mickey Mouse 4000 25 = 160 minutes.

Then calculate how much the difference between the two of them is if Mickey Mouse reaches the finish line: speed difference * time = distance difference.

Because Mickey Mouse arrives first, the time to use Mickey Mouse is (25-20)*160=800 meters.

The remote control sends a command, and Mickey Mouse rewinds 1*10%*25*1=m.

According to the unclear title, I will give two explanations:

The first type: the remote control is reset to zero every n times in a row, that is, Donald Duck first presses Mickey Mouse to go back one minute at 1*10% of the original speed, and Donald Duck presses it again at the interval time, Mickey Mouse also goes back one minute with 1*10% of the original speed, and only by letting Donald Duck press it again can make Mickey Mouse go back one minute at n*10% of the original speed. If this is the case, the minimum number of commands to be given is n*10%*25*1 minute=800 meters, n=320 times.

The second type: the remote control is pressed n times to accumulate, that is, Donald Duck presses Mickey Mouse once to rewind one minute at 1*10% of the original speed, and Donald Duck presses again at the interval time, and Mickey Mouse rewinds by 2*10% of the original speed for one minute, so that Donald Duck presses n times to make Mickey Mouse rewind N minutes at the original speed of n*10%. If this is the case, the minimum number of times an order can be given is:

1*10%*25*1+2*10%*25*1+3*10%*25*1+ -n*10%*25*1=320

1+2+3+--n=320 Since the sum of n=25 is calculated 1+2+3+--n=325>320, because the regression distance can only be large and not small, so n=25 times !!

In other words, Mickey Mouse's total movement (running forward minus running backward) in a 200-minute period cannot exceed 4,000 meters.

Suppose Donald Duck presses n times, then Mickey Mouse runs backwards for n minutes, leaving 200-n minutes to run forward.

The distance to be run is: 25*(200-n).

The distance to run backwards is: 1 * This is a formula).

The total distance is less than 4000 meters, that is: 25*(200-n)<4000 is reduced to: n*n+21n>800

You can try it, when n=19, n*n+21n=760, n=20, n*n+21n=820

Or solve the binary equation and derive, n >.

That is, press at least 20 times.