A water tank has two holes. The first hole alone empties the full tank in 9 minutes, and the second hole alone empties the full tank in 6 minutes. Assuming water leaks at a constant rate from each hole, how many minutes will it take for both holes together to empty the tank?

Introduction / Context:
This is a straightforward time and work style question framed in terms of two leaks. Each hole alone empties the tank in a known time, and we must compute the combined time when both holes are open together. The key idea is to add rates, not times.

Given Data / Assumptions:
- First hole empties the tank in 9 minutes
- Second hole empties the tank in 6 minutes
- Both holes leak water at constant rates
- Tank is initially full

Concept / Approach:
If a hole empties the tank in T minutes, its rate is 1/T of the tank per minute, considered as an outflow. When both holes are open, their outflow rates add. The combined time is then the reciprocal of the total outflow rate.

Step-by-Step Solution:
Step 1: Rate of first hole = 1/9 tank per minute. Step 2: Rate of second hole = 1/6 tank per minute. Step 3: Combined outflow rate = 1/9 + 1/6. Step 4: LCM of 9 and 6 is 18. So 1/9 = 2/18 and 1/6 = 3/18. Step 5: Combined rate = 2/18 + 3/18 = 5/18 tank per minute. Step 6: Time taken to empty tank with both holes open = 1 / (5/18) = 18/5 minutes. Step 7: 18/5 minutes = 3.6 minutes = 3 3/5 minutes.

Verification / Alternative check:
We can quickly confirm: In 3.6 minutes, the first hole alone would empty 3.6 / 9 = 0.4 of the tank, the second hole alone would empty 3.6 / 6 = 0.6 of the tank, and total emptied fraction = 0.4 + 0.6 = 1 full tank, matching the requirement.

Why Other Options Are Wrong:
3/5 minute: Much too small, giving only 0.2 of the tank emptied.
3 1/5 minutes (3.2 minutes) or 3 2/5 minutes (3.4 minutes): These give combined emptied fractions less than one, so the tank would not be completely empty.

Common Pitfalls:
A very common mistake is to average the times 9 and 6 instead of adding the rates, or to try to subtract one time from another. Remember that in all work and rate problems, we must work with rates (fractions per unit time) when tasks are performed simultaneously.

Final Answer:
Both holes together will empty the full tank in 3 3/5 minutes.