39. How far is it to school?

All the time while Alice and the Griffin were solving the previous problem, the Tortoise Quasi was weeping inconsolably.

- Can you tell me what is sad about this problem? - the Griffin barked at him angrily. - After all, the passenger caught up with the train. Or did I misunderstand something?
- Everything is correct, - agreed the Tortoise Quasi, - but we don't know what happened afterward! After all, judging by everything, the train could have derailed!
- No, just think about it! - Alice got angry. - First, they come up with all sorts of nonsense, and then they make a sad story out of everything!

The Tortoise Quasi did not answer, only grabbing his head with his front paws.

- Alright, - he said finally. - I will tell you a sad story. One morning, a boy had to go to school...
- That's sad! - agreed the Griffin.
- No, no! That's not sad, - objected the Tortoise Quasi. - The saddest part is still to come.

Alice and the Griffin listened to the whole story attentively but found nothing sad in it.

- So, - continued the Tortoise Quasi, - the father said to the boy: "Hurry up, or you'll be late for school!" - "I won't be late, Dad! - the boy replied. - I have everything calculated precisely. If I walk at a speed of four miles per hour, I will be five minutes late for the start of classes, but if I walk at a speed of five miles per hour, I will arrive ten minutes before the start of classes."

How far is it to school?
39. How far is it to school? The difference in time between being 5 minutes late and arriving 10 minutes before the start of the lesson is 15 minutes. Therefore, if the boy walks to school at a speed of 5 miles per hour, he will save 15 minutes (compared to how long it would take him to walk if he went at a speed of 4 miles per hour). Five miles per hour is one mile in 12 minutes, and 4 miles per hour is one mile in 15 minutes. Therefore, by walking faster, the boy saves 3 minutes per mile, and 15 minutes over a distance of 5 miles.

Thus, the school is 5 miles from home.

Verification. Walking at a speed of 5 miles per hour, the boy spends one hour on the journey, and walking at a speed of 4 miles per hour, he spends one hour and fifteen minutes (in one hour he covers the first 4 miles, and in a quarter of an hour, the last mile), that is, 1 hour and 15 minutes. The time difference is indeed 15 minutes.