Work-Rate Problems
📋 What it is
Work-rate problems add RATES, not times — if one pipe fills a tank in 4 h, its rate is ¼ tank per hour.
🗣️ Coach says
The trap in “two pipes fill a tank” problems is adding the TIMES (4 h + 6 h). Wrong! You add the RATES. Pipe A does ¼ per hour, pipe B does ⅙ per hour; together ¼ + ⅙ per hour. Convert to rates first.
🧠 Memory hook
Add RATES, never times. One job in t hours = 1/t of the job per hour.
😂 Giggle
Why is doubling and halving such a power couple?
Because 16 x 5 becomes 8 x 10 — same answer, half the effort!
😲 Whoa!
The same “add the rates” maths tells you how fast a bathtub drains while the tap runs, or how fast a team finishes a job — one idea, everywhere.
✅ Quick check: One pipe fills a tank in 4 h. What’s its rate per hour?
Say your answer out loud first — then reveal.
✏️ Check your work Sanity check: a combined rate must be BIGGER than either pipe alone — if your combined answer is slower than one pipe, you added times instead of rates.
¼ of the tank per hour — “one job in 4 hours” means 1/4 of the job each hour.
Rate = job ÷ time; you add rates (not times) when things work together.
🪄 Trick question: Two pipes fill a tank in 4 h and 4 h. Do they together take 8 h?
Careful — think it through, then reveal.
No — add RATES: ¼ + ¼ = ½ per hour, so together just 2 h. Adding times is the classic mistake.
Combining work means adding rates, which speeds things up, not adding times.
🧪 Try it! (2 minutes)
If you can wash 1 car in 20 min, what fraction do you wash in 1 min? (1/20 — that’s your rate.)
🔎 How did you work this?