Pipe Q can fill the tank in 60 hours while pipe R can fill it in 45 hours. Q and R pipes are opened together for 6 hours after which pipe W is also opened to empty the tank. All three pipes are opened simultaneously for 24 hours to reach the half level mark. How much time (in hours) will pipe W alone take to empty the entire tank?

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Step 1: Calculate the rates of pipes Q and R.
- Pipe Q fills the tank in 60 hours, so rate of Q = 1/60 tank/hour.
- Pipe R fills the tank in 45 hours, so rate of R = 1/45 tank/hour.

Step 2: Calculate the combined rate of Q and R.
- Combined rate of Q and R = 1/60 + 1/45 = (3 + 4)/180 = 7/180 tank/hour.

Step 3: Calculate the amount filled by Q and R in 6 hours.
- Amount filled in 6 hours = 6 * 7/180 = 42/180 = 7/30 tank.

Step 4: Let the rate of pipe W (emptying) be 1/x tank/hour.

Step 5: After 6 hours, all three pipes Q, R, and W are opened for 24 hours and the tank reaches half full.
- Amount filled in these 24 hours = 24 * (rate of Q + rate of R - rate of W) = 24 * (7/180 - 1/x).

Step 6: Total amount filled after 6 + 24 hours = 7/30 + 24 * (7/180 - 1/x) = 1/2 (half tank).

Step 7: Solve the equation:
7/30 + 24 * (7/180 - 1/x) = 1/2

Calculate 24 * 7/180 = (24 * 7)/180 = 168/180 = 14/15

So,
7/30 + 14/15 - 24/x = 1/2

Convert to common denominator 30:
7/30 + (14/15) = 7/30 + (28/30) = 35/30 = 7/6

So,
7/6 - 24/x = 1/2

Rearranged:
-24/x = 1/2 - 7/6 = (3/6 - 7/6) = -4/6 = -2/3

Multiply both sides by -1:
24/x = 2/3

Cross multiply:
24 * 3 = 2 * x
72 = 2x
x = 36

Step 8: x = 36 means pipe W empties the tank in 36 hours.

Step 9: Check options: 36 is option 3.

Therefore, pipe W alone will take 36 hours to empty the entire tank.

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