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Boats & Streams · Topic 5 of 5

🌊 Two Boats & Multi-step

2 exam question types, fully solved

The hardest questions put two boats on one river, or chain several steps together. They look scary but use nothing beyond and — you just apply them twice.

Two boats, and chaining the basics

• Same direction (a chase): when both boats run with the current, the stream pushes both equally and cancels. The gap closes at the difference of their speeds, and .

• Opposite directions (head-on): the gap closes at the sum of their speeds, .

• To isolate a current from a downstream run, subtract the boat's own speed: .

• Multi-step problems: first pin down and (or and ) from the given clues using and , then feed those into the fresh leg or round trip the question actually asks about.

⛵Boats & Streams SimulatorTwo boats · one current · watch the current cancel!
current →B₁B₂
Boat 1 still-water speed (B₁)
km/h
Boat 2 still-water speed (B₂)
km/h
Stream speed (S / current)
km/h
Starting gap between boats
km
Boat 1 over the ground (→)B₁ + S = 35 + 5 = 40 km/h
Boat 2 over the ground (→)B₂ + S = 25 + 5 = 30 km/h
Gap closes at the difference — the current cancels!
(B₁+S) − (B₂+S) = B₁ − B₂ = 35 − 25 = 10 km/h
The stream pushes both boats equally, so S vanishes — only still-water speeds matter between two boats.
Time to catch = gap ÷ difference
60 ÷ 10 = 6 h

Two boats run downstream at 35 and 25 km/h, the faster 60 km behind. The current cancels, so they meet after = h.

📝Practice Questions

Q1Two boats travel downstream at 40 km/h and 30 km/h, the faster one 50 km behind. How long until it catches up?

Q2Two boats move toward each other on a river at 12 km/h and 8 km/h, starting 40 km apart. They meet after:

Q3A boat at 8 km/h in still water goes downstream once on a 4 km/h current and once on a 2 km/h current. The ratio of its two downstream speeds is:

📚

Real exam questions — Two Boats & Multi-step

2 question types · 7 solved examples from real SSC papers

Advanced boats and streams: two boats sharing one river, plus multi-step problems that chain the downstream and upstream basics.

How to solve this type
Write each boat's real speed as D=b+sD=b+s (downstream) or U=b−sU=b-s (upstream). Same direction (a chase): closing speed == difference, so the stream term cancels. Opposite directions: closing speed == sum. Then time =gapclosing speed=\dfrac{\text{gap}}{\text{closing speed}}. To isolate a current, subtract the still-water speed: s=D−bs=D-b.

Two boats move downstream at 35 km/h and 25 km/h on a stream of 4 km/h. They start 60 km apart (faster boat behind). After how long does the faster boat catch the slower one?

A6 hB10 hC13 hD8 h

Boat A travels at 45 km/h and boat B at 36 km/h, both downstream. They are 81 km apart with A behind B. When do they meet?

A10 hB7 hC9 hD8 h

A man rows at 5 m/s in still water. He covers 200 m downstream in 10 s at high tide and in 25 s at low tide. Find the ratio of the two water (current) speeds.

A3:2B5:1C4:3D5:3

A boat's speed in still water is 8 km/h. It goes downstream once with a 4 km/h current and once with a 2 km/h current. Find the ratio of the two downstream speeds.

A6:5B3:2C12:10D4:3