Question

A tank can be filled by pipe P in 2 hours and pipe Q in 6 hours. At 10 am pipe P was opened. At what time will the tank be filled if pipe Q is opened at 11 am?

• A. 12:45 PM
• B. 5:00 PM
• C. 11:45 AM
• D. 11:50 AM

Hint:

Always calculate the work done by the first pipe before the second pipe joins the process.

Answer 1

The Correct Option is C

Concept: Work-time problems involve calculating rates: $Rate = 1 / Time$.

Step 1: Calculate rates.
- Pipe P rate = $1/2$ tank per hour. - Pipe Q rate = $1/6$ tank per hour.

Step 2: Calculate fill status at 11 am.
Pipe P works alone from 10 am to 11 am (1 hour). Tank filled = $1/2$. Remaining = $1/2$.

Step 3: Calculate time for both pipes.
Combined rate = $1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3$. Time = $Remaining / Rate = (1/2) / (2/3) = 3/4$ hours. $3/4 \text{ hours} = 45 \text{ minutes}$. equation 11 am + 45 minutes = 11:45 AM equation center 11:45 AM center