Wastewater · Worked step by step
What is the detention time of a 30,000 gallon tank?
If math has never been your thing, you are in the right place. Try it on paper first, then we write it out with you, one small step at a time, and explain every step in plain words so you never lose the thread.
The problem
A tank holds 30,000 gallons, and the flow through it is 10,000 gallons per hour. What is the detention time in hours?
Grab a pen and paper first
Give it a real try on paper before you watch. If you get stuck, take a hint. If you go blank, that is fine, press play and we will walk it through together.
Watch it solved, with you
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Press play and I’ll write it out with you, one small step at a time.
Every step gets a plain-words explanation here, so you always know exactly what just happened and why.
The written version, step by step
- 1
Write down what you know
volume = 30,000 gal • flow = 10,000 gal/hour
- The tank holds 30,000 gallons.
- 10,000 gallons flow through it every hour.
- We want to know how long a drop of water stays inside.
Quick trick: Notice the flow is per HOUR, so the answer will come out in hours.
- 2
Divide volume by flow
time = 30,000 ÷ 10,000
- Detention time = volume ÷ flow.
- Think of a bathtub: a big tub with a slow drain empties slowly.
- Put the numbers in: 30,000 ÷ 10,000.
Quick trick: Volume always goes on top, flow always on the bottom.
- 3
Do the division
time = 3 hours
- 30,000 ÷ 10,000. Cross off the matching zeros and it becomes 3 ÷ 1.
- That is just 3.
- So water stays in the tank about 3 hours.
Quick trick: Dividing round numbers? Cross off the same number of zeros from both: 30,000 ÷ 10,000 becomes 3 ÷ 1 = 3.
Remember this for good
Detention time = volume ÷ flow. It is how long a drop of water sits inside the tank.
Detention time is like a line at the store. The tank (volume) is how many people are in line; the flow is how fast the cashier serves them. Time in line = people ÷ speed = volume ÷ flow.
Solve it fast next time
- Detention time = volume ÷ flow. Volume on top, flow on the bottom.
- Keep the units matched: gallons ÷ gallons-per-hour = hours.
- If the volume is bigger than the flow, the time is more than 1. If flow is bigger, it is less than 1.
The answer: 3 hours.