Three pipes A, B, and C can fill a tank separately in 8 hours, 10 hours, and 20 hours, respectively. If all three are opened together, how long will they take to fill the tank?

Introduction / Context:With multiple inlets, the combined filling rate is the sum of individual rates. The time to complete one tank equals the reciprocal of the total rate.

Given Data / Assumptions:

• A fills in 8 h ⇒ rate = 1/8 tank/h.
• B fills in 10 h ⇒ rate = 1/10 tank/h.
• C fills in 20 h ⇒ rate = 1/20 tank/h.
• All three run together from empty to full.

Concept / Approach:Add the three rates, then invert to get time.

Step-by-Step Solution:Sum rate = 1/8 + 1/10 + 1/20.LCM(8,10,20) = 40 ⇒ 1/8 = 5/40, 1/10 = 4/40, 1/20 = 2/40.Total rate = (5 + 4 + 2)/40 = 11/40 tank/h.Time = 1 / (11/40) = 40/11 hours ≈ 3.636 hours.

Verification / Alternative check:Approximate hours: 3 hours 38 minutes (about 3 h 37 m). This aligns with 40/11 h.

Why Other Options Are Wrong:37/11, 47/11, 57/11 h correspond to incorrect numerator sums or mis-additions of rates.

Common Pitfalls:Using average of times instead of sum of rates; arithmetic slips in fractional addition.

Final Answer:40/11 h