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Boats & Streams · Topic 4 of 5

⏱️ Time Difference (same distance)

1 exam question type, fully solved

This is the single most-asked shape in the chapter: the same distance each way, with the upstream leg taking longer. From that time gap you can pull out the stream speed, the distance, or the boat-to-stream ratio.

Turn the time gap into the answer

Split the boat speed first: , . Then match the clue to a shortcut.

• Distance from a time gap : .

• Ratio from two times: for the same distance, — add the times for the boat part, subtract them for the stream part.

• “ times as long”: if the upstream time is times the downstream time, then , i.e. .

⛵Boats & Streams SimulatorSet speeds · watch the time gap appear
current →
Boat speed (B) in still water
km/h
Stream speed (S / current)
km/h
Downstream (→)B + S = 14 km/h
Upstream (←)B − S = 6 km/h
Time gap Δt — same distance each waykm
t↑ = d/U
10 h
60 ÷ 6
t↓ = d/D
4.29 h
60 ÷ 14
Δt = t↑ − t↓
5.71 h
10 − 4.29
The exam shortcut — given the gap Δt, find dh
d = D×U ÷ (D−U) × Δt
= 14×6 ÷ 8 × 2 = 10.5 × 2 = 21 km
(D − U = 2S, so the gap comes purely from the current)

With , and a 6 h gap, the distance = km.

📝Practice Questions

Q1A boat rows at 10 km/h in still water on a 2 km/h stream. Over 48 km, how much longer is the upstream leg than the downstream leg?

Q2Upstream takes 15 h and downstream 10 h over the same distance. The boat : stream speed ratio is:

Q3A boat at 15 km/h in still water takes twice as long upstream as downstream over the same distance. The stream speed is:

📚

Real exam questions — Time Difference (same distance)

1 question types · 5 solved examples from real SSC papers

For the same stretch each way, the upstream leg always lags the downstream leg, and that gap unlocks the stream speed, the distance, or the boat-to-stream ratio.

How to solve this type
Always split the boat speed first: downstream D=b+sD=b+s, upstream U=b−sU=b-s. Then pick the matching shortcut.
1) Distance from a time gap Δt\Delta t: d=D×UD−U×Δtd=\dfrac{D\times U}{D-U}\times\Delta t.
2) For the SAME distance, speed is inversely proportional to time, so b:s=(t<sub>up</sub>+t<sub>down</sub>):(t<sub>up</sub>−t<sub>down</sub>)b:s=(t<sub>up</sub>+t<sub>down</sub>):(t<sub>up</sub>-t<sub>down</sub>).
3) If upstream time is nn times downstream time, then bs=n+1n−1\dfrac{b}{s}=\dfrac{n+1}{n-1}, i.e. s=b×n−1n+1s=b\times\dfrac{n-1}{n+1}.

The speed of a boat in still water is 20 km/h and the stream flows at 8 km/h. The boat takes 6 hours more to go upstream than to come downstream over the same distance. Find that distance.

A336 kmB125 kmC120 kmD126 km

A boat takes 12 hours to go upstream and 8 hours to come downstream over the same distance. Find the ratio of the speed of the boat to the speed of the stream.

A10:2B5:2C5:1D7:3

A motorboat has a speed of 20 km/h in still water. It takes three times as long to travel a certain distance upstream as it does to travel the same distance downstream. Find the speed of the stream.

A10 km/hB8 km/hC15 km/hD12 km/h

A boat moves at 5 km/h in still water and the stream flows at 2.5 km/h. The distance each way is 15 km. How much more time does the boat take upstream than downstream?

A5 hB4 hC3 hD2 h

A boat can travel at 16 km/h in still water. It takes the same time to go 18 km upstream as it does to go 30 km downstream. Find the speed of the stream.

A7 km/hB4 km/hC5 km/hD6 km/h