Apprendre
Calculer le temps ou le nombre de travailleurs nécessaires quand le travail total reste constant.
Work rate problems are based on the formula: Work = Rate × Time, or equivalently, Work = Workers × Days. If the total work is constant, increasing workers decreases time proportionally. The key insight is that 'worker-days' (or 'machine-hours') represents the total work, and this stays the same regardless of how many workers do the job.
Total Work = Workers × Time. If W1 × T1 = W2 × T2, then T2 = (W1 × T1) / W2
- 4 workers in 12 days = 48 worker-days. 6 workers = 48 ÷ 6 = 8 days
- 3 machines in 10 hours = 30 machine-hours. 5 machines = 30 ÷ 5 = 6 hours
- 2 people in 15 days = 30 person-days. 5 people = 30 ÷ 5 = 6 days
Comment le reconnaître
- Problem mentions workers/machines and time to complete a job
- Asks how long with different number of workers
- Total work (job size) remains constant
Erreurs fréquentes
- Thinking more workers means more time (it's inverse)
- Adding workers instead of multiplying
- Forgetting that work = workers × time
Résolution étape par étape
5 ouvriers terminent un projet en 12 jours. Combien de jours pour 10 ouvriers ?
- Calculez le travail total : 5 ouvriers x 12 jours = 60 jours-ouvrier
- Le travail total reste constant à 60 jours-ouvrier
- Divisez par le nouveau nombre d'ouvriers : 60 / 10
- Calculez : 60 / 10 = 6 jours
Réponse: 6 days