One pipe can empty a tank in 12 minutes and another pipe can empty it in 16 minutes. If both outlet pipes are opened together, how long will it take to empty a full tank?

Introduction / Context:
When two outlets drain a tank simultaneously, their emptying rates add. The total time is the reciprocal of the combined rate.

Given Data / Assumptions:

• Outlet 1 empties in 12 minutes ⇒ rate = 1/12 tank/min.
• Outlet 2 empties in 16 minutes ⇒ rate = 1/16 tank/min.
• The tank is initially full and both outlets run together.

Concept / Approach:
Net emptying rate = 1/12 + 1/16. Time to empty = 1 / (net emptying rate).

Step-by-Step Solution:
LCM(12, 16) = 48.1/12 = 4/48; 1/16 = 3/48.Combined rate = (4 + 3)/48 = 7/48 tank/min.Time to empty = 1 / (7/48) = 48/7 minutes ≈ 6.857 minutes.

Verification / Alternative check:
Approximate check: 7 minutes at 7/48 per minute would drain 49/48 > 1 tank; slightly less than 7 minutes is consistent with 48/7.

Why Other Options Are Wrong:
6 minutes is too short; 7 minutes is a rounded overestimate; 8 minutes is clearly too long.

Common Pitfalls:
Adding times instead of rates or miscomputing the LCM when adding fractions.

Final Answer:
48/7 minutes