The boy lived far from his school and rode his bicycle to it. He was a great pedantic and used "number" everywhere 1 measure ".

One day he traveled halfway at that speed, that the wheel of the bicycle was doing 2 revolutions per second, and he traveled the other half at that speed, that the wheel of the bicycle was doing 3 turnover on 2 seconds. It took him all the way 35 minutes. The boy thought to himself, that if he traveled half way with speed 2 wheel rotation on 1 a second, and the other half of the way at speed 3 wheel rotation on 2 seconds, then the average speed was 5 wheel rotation on 3 seconds - and that was the speed he drove home. However, it turned out, that the way back took 36 minutes, and not 35, as expected.

The boy thought to himself, that he must have slowed down involuntarily and therefore lost one minute.

On the second day, the boy traveled halfway at speed 2 wheel revolutions per second, and the other half at speed 3 revolutions per second and then the whole journey took him 25 minutes. The boy told himself, that he would be working on his way back 5 wheel rotation on 2 seconds, or 2y turns per second. Instead of what you expected 25 He only drove for minutes 24 minutes.

And he thought to himself again, that he probably picked up the pace involuntarily and that is why he "made up" one minute. But it surprised him nonetheless, that when he was driving slowly yesterday, it still slowed down, and today - when driving fast - he picked up the pace even more.

So he set about calculating, to check, what is the source of the discrepancy between the facts and the predictions.

He measured the length of the wheel circumference of the bicycle; was 2,25 m. On the first day, he was going home at speed 5 wheel rotation on 3 seconds; it was easy to calculate, that the speed was 3,75 m per second, or 225 m per minute. And because the way back was on 36 minutes, so the length of the road was 8100 m.

And how was it yesterday with the ride there, to school? The first half of the way, or 4050 m, he was driving at speed 2 wheel revolutions per second, or 4,50 m per second; the first half of the way was taken 4050 :4,50 = 900 seconds, or 15 minutes. The other half of the way he was driving at speed 3 turns on 2 seconds, or 3,375 m per second; the other half of the way took him 4050 : 3,375 = 1200 seconds, or 20 minutes. Together, it took the whole way to school 15 + 20 = 35 minutes, and not 36 minutes!

Where with, hell, this minute has passed?

Let us recall, how a boy calculated the average speed of travel:

2 obroty na 1 sec.

3 obroty na 2 sec.

5 obrotów na 3 sec.

or 1 rotation on 3/5 seconds.

Now let's calculate the average speed differently. In the first half of the way, the boy was driving at speed 2 turns on 1 a second, or 1 rotation for j seconds, and on the other half of the road he was driving at speed 3 turns on 2 seconds, or 1 rotation on 2/3 seconds. On average he did 2 turnover on 1/2 + 2/3= 7/6 seconds, or 1 rotation on 7/12 seconds.

The whole way was 8100 m, or 8100 : 2,25 = 3600 wheel rotation, and because 1 the turnover continued 7/12 seconds, so on 3600 turnover was needed 3600 • 7/12 = 2100 seconds, or 35 minutes.

Everything is fine! You just need to correctly calculate the average driving speed.

Now let's do the calculations for the second day.

The first half of the way at speed 2 revolutions per second, i.e.. 4,50 m per second, took 4050 : 4,50 = 900 sec, or 15 min. The other half of the way at speed 3 revolutions per second, it means 6,75 m per second, took 4050 : 6,75 = 600 sec, or 10 min. The whole road took 10 + 15 = 25 minutes.

Let's calculate the average travel speed with our new method.

1 rotation , on 1/2 sec.

1 rotation on 1/3 sec.

2 turnover on 5/6 sec.

or 1 rotation on 5/12 seconds.

We already know, that the whole road required 3600 wheel rotation, what's wearing 5/12 sec. for one revolution it requires 1500 sec, or 25 min. - in full accord with the prediction.