Problem: Time to Drain a Reservoir with Pipes

What you're solving for

You are solving for the time it takes for 6 large pipes and 6 small pipes to drain a reservoir together.

What's given in the problem

6 large pipes drain the reservoir in 12 hours.

6 small pipes drain the reservoir in 18 hours.

How to solve

Calculate the individual drainage rates and then combine them to find the combined rate and time.

Step 1: Calculate the drainage rate of 6 large pipes

Rate of 6 large pipes: RL = 1 reservoir / 12 hours

Step 2: Calculate the drainage rate of 6 small pipes

Rate of 6 small pipes: RS = 1 reservoir / 18 hours

Step 3: Calculate the combined drainage rate

Combined rate: Rtotal = RL + RS

Rtotal = 1/12 + 1/18

Rtotal = 3/36 + 2/36 = 5/36 reservoir/hour

Step 4: Calculate the time to drain the reservoir with both sets of pipes

Time T = 1 reservoir / Rtotal

T = 1 / (5/36) = 36/5 hours

T = 7.2 hours