Two pipes A and B can fill a tank in 18 hours and 6 hours, respectively. If both are opened together from empty, how much time is needed to fill the tank?

Introduction / Context:
For simultaneous inlets, add rates to get the total rate. The filling time equals the reciprocal of that total rate.

Given Data / Assumptions:

• A fills in 18 h ⇒ 1/18 tank/h.
• B fills in 6 h ⇒ 1/6 tank/h.

Concept / Approach:
Total rate = 1/18 + 1/6 = 1/18 + 3/18 = 4/18 = 2/9 tank/h. Time = 1 ÷ (2/9) = 9/2 h.

Step-by-Step Solution:
Sum rates: 1/18 + 1/6 = 4/18 = 2/9.Time = 1 ÷ (2/9) = 9/2 hours = 4.5 hours = 4 1/2h.

Verification / Alternative check:
Check: In 4.5 h, A fills 4.5/18 = 0.25 tank; B fills 4.5/6 = 0.75 tank; total = 1 tank.

Why Other Options Are Wrong:
7, 6, 10 h are inconsistent with the combined rate 2/9 tank/h.

Common Pitfalls:
Adding times, not rates; mis-converting 4.5 hours to mixed fraction.

Final Answer:
4 1/2h