Pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both are opened together into an empty tank, how long will they take to fill it?

Introduction / Context:
When two inlets run together, their rates add. The time to complete one tank equals the reciprocal of the combined rate.

Given Data / Assumptions:

• A fills in 10 h ⇒ 1/10 tank/h.
• B fills in 15 h ⇒ 1/15 tank/h.

Concept / Approach:
Combined rate = 1/10 + 1/15. Time = 1 ÷ (combined rate).

Step-by-Step Solution:
LCM(10, 15) = 30 ⇒ 1/10 = 3/30; 1/15 = 2/30.Total rate = (3 + 2)/30 = 5/30 = 1/6 tank/h.Time to fill = 1 ÷ (1/6) = 6 hours.

Verification / Alternative check:
In 6 hours, A fills 6/10 = 3/5 and B fills 6/15 = 2/5; total = 1 tank.

Why Other Options Are Wrong:
12 1/2 hours is slower than either pipe alone; 5 hours is too optimistic for these rates.

Common Pitfalls:
Adding times instead of rates; arithmetic errors in LCM.

Final Answer:
6 hours