Question

Valve A fills a bathtub in 10 hours and valve B fills it in 15 hours. A and B are opened together; later B is closed. The tub is filled in 8 hours in total. For how long was B open?

• A. 1 hour
• B. 2 hours
• C. 3 hours
• D. 4 hours

Hint:

In mixed-time problems, translate to rates, write a single “total work = 1” equation, and solve for the unknown time.

Answer 1

The Correct Option is C

Rates: A fills \(1/10\) of the tub per hour; B fills \(1/15\) per hour.
Let B be open for \(t\) hours. A is open the whole \(8\) hours.
Work equation: \[ \underbrace{8\cdot\frac{1}{10}}_{\text{A's work}} \;+\; \underbrace{t\cdot\frac{1}{15}}_{\text{B's work}} \;=\;1. \] So \(\frac{8}{10}+\frac{t}{15}=1\). Hence \(\frac{t}{15}=1-\frac{8}{10}=\frac{1}{5}\), giving \(t=3\ \text{hours}\).
[2mm] \[ \boxed{3\ \text{hours}} \]