11.
Texas Instruments technical mcq question, verified with a worked answer. Free to practise - no sign-up.
Capacity of the pool**
You are asked to use two pipes P1 and P2 to fill a pool that has another pipe P3 at the bottom of it. It is given that pipes P1 and P2 can fill the tank in 10 and 20 minutes, respectively and pipe P3 can empty 12 gallons per minute from the pool.
What is the capacity of the pool if all three pipes working together can fill the tank in 30 minutes?
Note: Choose the option that coincides with the nearest integer.
Show answer & explanation
The net rate of filling the pool is the sum of the rates of P1 and P2 minus the rate of P3. By setting the net rate equal to the reciprocal of the total time taken (1/30), we can solve for the total capacity V.
Step-by-step Derivation:
Step 1: Define V as the capacity of the pool in gallons.
Step 2: Determine the rates of the pipes in terms of pool capacity per minute.
- Rate of P1 = V / 10
- Rate of P2 = V / 20
- Rate of P3 = 12 gallons/minute (emptying)
Step 3: Set up the equation for the combined rate when all three pipes are open.
Net Rate = Rate(P1) + Rate(P2) - Rate(P3)
Net Rate = V/10 + V/20 - 12
Step 4: We are given that the pool is filled in 30 minutes, so the Net Rate is also V / 30.
V/30 = V/10 + V/20 - 12
Step 5: Solve for V.
12 = V/10 + V/20 - V/30
Find a common denominator for the fractions (60):
12 = (6V + 3V - 2V) / 60
12 = 7V / 60
Step 6: Calculate V.
7V = 12 * 60
7V = 720
V = 720 / 7
V ≈ 102.857 gallons
Step 7: Round to the nearest integer as requested.
V ≈ 103 gallons.