Math · Stage 6

Solve combined rate and work problems

Two helpers at once don't add their times — they add their rates. Pick a shared whole, add how much each does per hour, then divide to get the time together.

✦ Math📘 Stage 6 · S6⏱ ~14 min🧒 Ages 10–12★ Free to start

I can solve combined rate and work problems.

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Kavi Fills the Tub 🪣

Kavi's garden tub fills from one hose in 6 minutes 💧 — but little Pip's hose fills the same tub in 3 minutes! “Two hoses at once must be faster,” said Kavi. “Think of the tub as 6 cupfuls: each minute I pour 1 and Pip pours 2 — together 3 a minute, so 6 ÷ 3 = 2 minutes! You add the rates, not the times — that's the secret of combined work.”

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What your child will learn

1Two workers add their speedsKavi pours 3 litres a minute 💧 and Pip pours 5. Working at the same time, their speeds simply add: 3 + 5 = 8 litres every minute.

2Add the rates — never the timesKavi paints a fence in 6 h, Pip in 3 h. Tap each card: one way is a trap, one way is right.

3Turn the rates into a timeShare the fence as 6 equal parts. Each hour Kavi paints 1 part and Pip paints 2 — together 3 parts an hour.

4A drain is a take-away rateA drain removes water, so its rate is subtracted. Compare how fast each tank fills with how fast it drains, then sort it →

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A peek inside

Kavi fills a tub in 6 min 💧; Pip fills the same tub in 3 min. Working together, how long?

share the tub as 6 cupfuls: Kavi pours 1/min, Pip 2/min → together 3/min; 6 ÷ 3

Try this at home: Add the rates: Kavi pours 7 L/min, Pip pours 8 L/min → how many litres a minute together?

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

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Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.