Problèmes de Cadence

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

Conseils de pratique

Raisonnement Numérique