Joan, Jordi, Laura, Marta, Cecilia

 

You and your mates want to go from La Senìa to Genova. You are driving a fast car, while your mates are moving on a slow bus that can move at a speed that is 1/10 of your speed.

Your mates on the bus challenge you to a race, claiming that they on the bus would win as long as you on the fast car give them a small head start. You laugh at this, for of course you are driving a fast car, whereas the bus is heavy and slow.

“How big a head start do you need?” you ask them with a smile.

“One hundred kilometers,” they reply.

You laugh louder than ever. “You will surely lose, my friends, in that case,” you tell your mates, “but let us race, if you wish it.”

“On the contrary,” say them, “I will win, and I can prove it to you by a simple argument.”

“Go on then,” you reply, with less confidence than you feel before. You know you are driving a faster car, but you also know your mates have the sharper wits, and you had lost many a bewildering argument with them before this.

“Suppose,” begin your mates, “that you give me a 100-kilometer head start. Would you say that you could cover that 100 kilometers between us very quickly?”

“Very quickly,” you affirm.

“And in that time, how far should we have gone, do you think?”

“Perhaps a kilometer—no more,” you say after a moment’s thought.

“Very well,” reply your mates, “so now there is a kilometer between us. And you would catch up that distance very quickly?”

“Very quickly indeed!”

“And yet, in that time we shall have gone a little way farther, so that now you must catch that distance up, yes?”

“Ye-es,” you say slowly.

“And while you are doing so, we shall have gone a little way farther, so that you must then catch up the new distance,” your mates continue smoothly.

You say nothing.

“And so you see, in each moment you must be catching up the distance between us, and yet and we — at the same time—will be adding a new distance, however small, for you to catch up again.”

“Indeed, it must be so,” you say wearily.

“And so you can never catch up,” your mates conclude sympathetically.

“You are right, as always,” you say sadly—and concede the race.

Are your school mates right? How can you deduce your decision? Use a spreadsheet or any mean to prove your decision and prepare a presentation explaining to your mates what you learned.