Count inlets vs outlets from net fill time Seven pipes connect to a tank; some are inlets (each fills in 10 h) and some are outlets (each empties in 15 h). When all seven are opened together, the tank fills in 2 8/11 hours. How many inlets and how many outlets are there?

Introduction / Context:
When identical inlets and outlets are mixed, the net rate is (number of inlets * inlet rate) − (number of outlets * outlet rate). With a known net fill time, we can solve a pair of linear equations for the counts.

Given Data / Assumptions:

• Total pipes = 7.
• Each inlet: 10 h ⇒ 1/10 per hour.
• Each outlet: 15 h ⇒ 1/15 per hour (negative).
• Net fill time = 2 8/11 h = 30/11 h ⇒ net rate = 11/30 per hour.

Concept / Approach:
Let i = inlets and o = outlets with i + o = 7. Then i/10 − o/15 = 11/30. Solve the linear system.

Step-by-Step Solution:

Verification / Alternative check:
Net rate = 5*(1/10) − 2*(1/15) = 1/2 − 2/15 = (15 − 4)/30 = 11/30 ⇒ time = 30/11 h.

Why Other Options Are Wrong:
Any other split fails the linear system.

Common Pitfalls:
Using 2 8/11 as 2.8 recurring instead of 30/11; always convert mixed fractions to improper ones.

Final Answer:
5, 2