Math · Stage 5

Boats-in-stream problems

A river current speeds a boat up going one way and slows it down the other. From the two measured speeds you can uncover the boat's true still-water speed AND the hidden speed of the current — a classic olympiad trick.

✦ Math📘 Stage 5 · S5⏱ ~14 min🧒 Ages 9–10★ Free to start

I can solve boats-in-stream (current) problems.

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Kavi and the Secret River 🚣

Kavi paddles downstream at 14 km/h, then turns and crawls upstream at only 6 km/h. "The river pushed me one way and fought me the other," says Kavi. "From those two speeds I can find how fast I really row and how fast the current flows — watch!"

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What your child will learn

1Downstream is fast, upstream is slowA boat has one still-water speed (how fast it rows in a calm lake). On a river the current changes what you measure: going with the current (downstream) you add the current, going against it (upstream) you subtract it. Tap each card.

2Still water sits exactly in the middlePut the two measured speeds on a line: upstream 6 at the slow end, downstream 14 at the fast end. The boat's still-water speed is the number exactly halfway between them — here 10. The current is how far each measured speed is from that middle: 4 each way.

3Two formulas that unlock any river

4Down + Up splits into two equal boatsAdd the speeds: 14 + 6 = 20. The current cancels — it was added once and subtracted once — so what is left is the boat counted twice. Split 20 into two equal parts and each part is the still-water speed, 10. Tap ◀ less / more ▶.

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A peek inside

A boat's speed is 14 km/h downstream and 6 km/h upstream. Find its speed in still water.

still water = (down + up) ÷ 2 = (14 + 6) ÷ 2 = 20 ÷ 2

Try this at home: A boat goes <b>15 km/h downstream</b> and <b>9 km/h upstream</b>. Still-water speed = __ km/h

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 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.