All three inlets running together Pipes A, B and C can fill a tank in 5 h, 6 h and 30 h, respectively. If all three are opened together, how long will the tank take to fill completely?

Introduction / Context:When several inlets fill the same tank, their constant rates add linearly. The total time is the reciprocal of the combined rate.

Given Data / Assumptions:

• A fills in 5 h ⇒ 1/5 per hour.
• B fills in 6 h ⇒ 1/6 per hour.
• C fills in 30 h ⇒ 1/30 per hour.
• All are inlets (Recovery: original options inconsistent; repaired keeping intent unchanged).

Concept / Approach:Sum the three positive rates to get the net fill rate, then invert to get time.

Step-by-Step Solution:

Verification / Alternative check:In 2.5 h, A adds 0.5 tank, B adds 2.5/6 ≈ 0.4167, C adds 2.5/30 ≈ 0.0833; total = 1 tank.

Why Other Options Are Wrong:33/14 ≈ 2.357 and 39/14 ≈ 2.786 are off; 3 h is too slow given the extra inlet.

Common Pitfalls:Confusing a filler with an outlet or averaging times instead of adding rates.

Final Answer:5/2 h