P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
🕒 Work and Time Calculation 🕒
P’s work rate = 1/12 (work done per 8-hour day)
Q’s work rate = 1/8 (work done per 10-hour day)
To compare their work rates, convert Q’s work rate to an 8-hour day:
Q’s work rate (per 8-hour day) = (1/8) × (8/10)
= 1/10 (work done per 8-hour day)
Combined work rate of P and Q = P’s work rate + Q’s work rate
= 1/12 + 1/10
= (5 + 6) / 60
= 11/60 (work done per 8-hour day)
Time taken by P and Q to complete the work = 1 / Combined work rate
= 1 / (11/60)
= 60/11
= 5.45 days (approximately)
🎉 P and Q can complete the work together in approximately 5.45 days. 🕒
