## A maths question in French for intermediate learners to practice.

Sophia décide de faire une course à bicyclette avec son amie Linda. Comme Sophia est plus rapide, elle laisse à son amie 30 minutes d’avance. Si Sophia roule à une vitesse moyenne de 30 km/h et que Linda va à 25 km/h, après combien de temps se rejoindront-elles et quelle distance leur restera–t-il à parcourir, si la course est de 90 km?

## 29 Comments

- 1513

Malheureusement je suis NUL NUL NUL en mathématiques à l'école, alors je ne peux pas calculer tout ça même en ma langue maternelle. :/ Mais résoudre des problèmes de maths en une langue étrangère peut être très utile pour pratiquer cette langue (au moins pour ceux/celles qui ont des connaissances suffisantes en maths). :-)

- 1513

Enfin! Quelqu'un qui peut me comprendre! En septembre je serai en seconde (au lycée) et je ne peux pas résoudre un tel problème en maths! :o (bien que je sois fort en langues :D)

Fantastique!

Linda avance (25 km/h) * (0,5 h) = 12,5 km après son amie commence. Cette distance diminue 5 km par heure. Elles sont ensemble dans (12,5 km) / (5 km/h) = 2,5 heures plus tard (depuis Sophia a commencé). La distance que reste est (90 km) - (30 km/h)*(2,5 h) = 15 km.

En anglais (parce qu'il ya beaucoup de erreurs en français):

Linda advances 12.5 km before her friend start. That distance decreases by 5 km per hour. They are together **2.5 hours** later from the time that Sophia started, or 3 hours from the time that Linda started. The remaining distance is **15 km.**

Another way to think about the problem. Let t=0 denote the time that Sophia starts. Then at any positive value of t, Linda has traveled a distance of 25 x t+12.5 km (or 25 x t+25 x 0.5) and Sophia has traveled a distance of 30 x t km. We can then set these distances equal to each other and solve for t.

25 x t + 12.5 = 30 x t

t=2.5 hr

It is the same result as DonFiore gave, just a little different way to think about the problem.

Right, but it is ambiguous as to when we start the clock. If Linda left thirty minutes ago and Sophia leaves right now, they will meet up again 2.5 hrs from now. If Linda leaves right now, and Sophia will stand around for the next thirty minutes, they will meet up again in 3 hrs.

The solution is at http://archimede.mat.ulaval.ca/amq/bulletins/dec08/Chronique_enigmes%28dec08%29.pdf. Both values are given, the amount of time after Linda starts and the amount of time after Sophia starts. Notice it says "Sophia rejoindra Linda apres 2,5 heures, donc 3 heures apres le depart de Linda."

I'm very tempted to say, mathematically, that I agree with you! However, as we are supposed to be learning French, and at the risk of seeming very boorish and pedantic ... :

It is important to recognise that the verb "rejoindre". as used in the solution linked to, is transitive. This means there is a subject A performing the action "rejoindre" on object B. So it is OK to use it to mean Sophia (A) "catches up with" Linda (B) after 2.5 hours.

However, "se rejoindre" is a different kettle of fish. The "se" prefix turns it into a pronominal, reciprocal verb. Reciprocal verbs require two or more subjects (Sophia and Linda) and these parties are also the objects of the action in equal measure. As it is not possible for Sophia to meet Linda after 2.5 hours, but Linda to meet Sophia 3 hours after their last meeting, the only grammatically logical answer is to include Sophia's waiting time in the time they have been apart.

Good argument, but you are forgetting that it takes Sophia 3 1/2 hours to finish the race; 30 minutes waiting time, plus 3 hours riding time. So after only 3 hours, she **does** catch up with Linda before she finishes the race.

Or look at it the other way around. If they start the race together, Sophia reaches the finish line in 3 hours, but Linda takes (90 km / 25 km/h) = 3.6 hours. So over the 90 km course, they have been apart for 3.6 hours.

If they instead stop the race at the 75 km point, Sophia gets there in less than 3 hours, but Linda still needs (75 km / 25 km/h) = 3 hours. They have been apart for 3 hours, whether Sophia waits at the beginning or the end of the race.