Boats and Streams Problems with Solutions Wisdom Helps

Aptitude · Time, Speed & Distance

Boats &
Streams, made clear.

Master upstream and downstream problems with simple rules, worked examples, exam shortcuts, and a 15-question quiz that checks your answers as you go.

Maths Classes by Mahesh SirConcepts · Formulas · Practice8 min read

01 · Understand the current02 · Learn the formulas03 · Try 15 MCQs

In this lesson

1. The core idea
2. Essential formulas
3. 10 solved examples
4. Shortcuts & exam checks
5. 15-question quiz
6. What to study next
7. Quick revision

01 · Start with the idea

The stream either helps or resists

A boat has its own speed in still water. A flowing river adds to that speed when the boat goes with the current, and takes away from it when the boat moves against the current.

↓ Downstream · with the current

The boat and water move in the same direction, so their speeds add.

↑ Upstream · against the current

The boat moves against the flow, so the stream speed is subtracted.

Quick memory cue: Downstream = with the stream = add. Upstream = against the stream = subtract.

02 · Keep these close

The essential formulas

Let B be the boat’s speed in still water, S the stream speed, D the downstream speed, and U the upstream speed.

Downstream speed

D = B + S

Upstream speed

U = B − S

Boat speed in still water

B = D + U2

Stream speed

S = D − U2

Time

T = distancespeed

Distance

distance = speed × time

Speed

speed = distancetime

Average speed · equal distances

2DUD + U

Important: Use the average-speed shortcut only when the downstream and upstream distances are equal. For unequal distances, calculate total distance ÷ total time.

1 hour = 60 minutes 1 km/h = 518 m/s 1 m/s = 185 km/h

03 · Learn by seeing it work

10 solved examples

All 10 questions, worked solutions, and final answers are shown below—no opening or tapping required.

01

Find downstream speed

QuestionA boat travels at 15 km/h in still water; the stream flows at 4 km/h. Find its downstream speed.

Given

Boat speed in still water B = 15 km/h; stream speed S = 4 km/h. Find the downstream speed.

Concept

Going downstream, the current pushes the boat forward, so the stream speed is added to the boat speed.

Step-by-step solution

1. Downstream speed = B + S
2. = 15 + 4
3. = 19 km/h

Answer: 19 km/h Shortcut: Downstream means add. Check: 19 km/h is faster than the still-water speed of 15 km/h, which makes sense because the current is helping.

02

Find upstream speed

QuestionA boat's speed in still water is 20 km/h and stream speed is 6 km/h. Find its upstream speed.

Given

B = 20 km/h; S = 6 km/h. Find the upstream speed.

Concept

Going upstream, the current pushes against the boat, so the stream speed is subtracted from the boat speed.

Step-by-step solution

1. Upstream speed = B − S
2. = 20 − 6
3. = 14 km/h

Answer: 14 km/h Shortcut: Upstream means subtract. Check: 14 km/h is slower than 20 km/h, as expected. Reverse check: downstream = 20 + 6 = 26, and 26 + 142 = 20 = B ✓.

03

Find boat speed and stream speed

QuestionA boat's downstream speed is 18 km/h and upstream speed is 10 km/h. Find its speed in still water and the stream speed.

Given

Downstream speed D = 18 km/h; upstream speed U = 10 km/h. Find B and S.

Concept

We know D = B + S and U = B − S. Adding the two equations cancels S, giving D + U = 2B. Subtracting them cancels B, giving D − U = 2S.

Step-by-step solution

1. B = D + U2 = 18 + 102 = 282 = 14 km/h
2. S = D − U2 = 18 − 102 = 82 = 4 km/h

Answer: Boat speed = 14 km/h · Stream speed = 4 km/h Shortcut: Add and halve for the boat; subtract and halve for the stream. Check: 14 + 4 = 18 ✓ (downstream) and 14 − 4 = 10 ✓ (upstream).

04

Find downstream travel time

QuestionA boat travels 60 km downstream at 15 km/h. How long does the journey take?

Given

Distance = 60 km downstream; the boat's downstream speed is 15 km/h. Find the time taken.

Concept

Time = distancespeed. The 15 km/h is already the downstream speed, so the stream is already included — do not add or subtract it again.

Step-by-step solution

1. Time = 6015
2. = 4 hours

Answer: 4 hours Shortcut: When the speed given is already a downstream or upstream speed, go straight to distance ÷ speed. Check: 15 km/h × 4 h = 60 km ✓.

05

Find upstream travel time

QuestionA boat's speed in still water is 12 km/h and the stream speed is 3 km/h. How long does it take to travel 45 km upstream?

Given

B = 12 km/h; S = 3 km/h; distance = 45 km upstream. Find the time taken.

Concept

This needs two steps: first find the upstream speed, then divide the distance by it.

Step-by-step solution

1. Upstream speed = B − S = 12 − 3 = 9 km/h
2. Time = distanceupstream speed = 459 = 5 hours

Answer: 5 hours Shortcut: Speed first, time second — never divide the distance by the boat speed alone. Check: 9 km/h × 5 h = 45 km ✓. (Using 12 km/h would wrongly give 3.75 hours.)

06

Equal-distance round trip: time and average speed

QuestionA boat travels 30 km downstream at 15 km/h, then returns 30 km upstream at 10 km/h. Find the total time and average speed.

Given

30 km downstream at D = 15 km/h, then 30 km back upstream at U = 10 km/h. Find the total time and the average speed.

Concept

Average speed is always total distance ÷ total time. Because the two distances are equal, the shortcut 2DUD + U gives the same result.

Step-by-step solution

1. Downstream time = 30 ÷ 15 = 2 hours
2. Upstream time = 30 ÷ 10 = 3 hours
3. Total time = 2 + 3 = 5 hours
4. Total distance = 30 + 30 = 60 km
5. Average speed = 60 ÷ 5 = 12 km/h

Answer: Total time = 5 hours · Average speed = 60 ÷ 5 = 12 km/h Shortcut: 2 × 15 × 1015 + 10 = 30025 = 12 km/h. Check: The simple mean (15 + 10) ÷ 2 = 12.5 km/h is wrong, because the boat spends more time at the slower upstream speed.

07

Find stream speed from travel times

QuestionA boat covers 24 km downstream in 2 hours and the same distance upstream in 3 hours. Find the stream speed.

Given

Downstream: 24 km in 2 hours. Upstream: 24 km in 3 hours. Find the stream speed.

Concept

Convert each trip to a speed first using speed = distancetime, then use S = D − U2.

Step-by-step solution

1. D = 242 = 12 km/h
2. U = 243 = 8 km/h
3. S = D − U2 = 12 − 82 = 42 = 2 km/h

Answer: 2 km/h Shortcut: Two trips with the same distance → find D and U, then halve the difference. Check: B = 12 + 82 = 10 km/h, and 10 + 2 = 12 ✓, 10 − 2 = 8 ✓.

08

Find distance in both directions

QuestionA boat's speed in still water is 16 km/h and stream speed is 4 km/h. Find the distance travelled downstream in 3 hours and upstream in 2 hours.

Given

B = 16 km/h; S = 4 km/h. Find the distance covered downstream in 3 hours and upstream in 2 hours.

Concept

The two directions have different speeds, so work them out separately, then use distance = speed × time.

Step-by-step solution

1. Downstream speed = 16 + 4 = 20 km/h
2. Downstream distance = 20 × 3 = 60 km
3. Upstream speed = 16 − 4 = 12 km/h
4. Upstream distance = 12 × 2 = 24 km

Answer: Downstream = 60 km · Upstream = 24 km Shortcut: Never multiply the boat speed (16) by the time directly — the stream always changes the effective speed. Check: 6020 = 3 h ✓ and 2412 = 2 h ✓.

09

Find boat speed and stream speed from two speeds

QuestionThe downstream speed is 26 km/h and upstream speed is 14 km/h. Find boat speed in still water and stream speed.

Given

D = 26 km/h; U = 14 km/h. Find the boat speed in still water and the stream speed.

Concept

Use the sum-and-difference formulas: B = (D + U) ÷ 2 and S = (D − U) ÷ 2.

Step-by-step solution

1. B = 26 + 142 = 402 = 20 km/h
2. S = 26 − 142 = 122 = 6 km/h

Answer: Boat speed = 20 km/h · Stream speed = 6 km/h Shortcut: B sits exactly halfway between D and U; S is the gap from B to either of them. Check: 20 + 6 = 26 ✓ and 20 − 6 = 14 ✓.

10

Find total time for a round trip

QuestionA boat travels 36 km downstream at 12 km/h and returns 36 km upstream at 9 km/h. Find the total journey time.

Given

36 km downstream at D = 12 km/h and 36 km back upstream at U = 9 km/h. Find the total journey time.

Concept

Total time is the sum of the two separate times, each found with time = distancespeed.

Step-by-step solution

1. Downstream time = 3612 = 3 hours
2. Upstream time = 369 = 4 hours
3. Total time = 3 + 4 = 7 hours

Answer: 7 hours Shortcut: Add the times, not the speeds. Check: Average speed = 727 ≈ 10.29 km/h, and the shortcut 2 × 12 × 912 + 9 = 21621 ≈ 10.29 km/h gives the same value ✓.

04 · Faster exam solving

Shortcuts & exam checks

01If D and U are given, B = D + U2 and S = D − U2.

02If B and S are given, add for downstream and subtract for upstream.

03When distance and time are given, first find speed = distancetime.

04Equal distances in opposite directions? Use 2DUD + U, not the simple mean.

05If downstream and upstream speeds are equal, stream speed is zero.

06A positive upstream speed requires boat speed in still water to be greater than stream speed.

07Check what the question asks for: boat speed, stream speed, time, distance, or average speed.

08Keep units consistent. Convert minutes to hours before using a speed in km/h.

05 · Your turn

15-question practice quiz

Start the timer, pick an option and check it. You get instant feedback with a full explanation, and a result summary when you finish.

0/15Correct

Time00:00

06 · Keep building

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07 · One-minute recap

Quick revision

Four rules to remember

• Downstream speed = B + S
• Upstream speed = B − S
• Boat speed = D + U2
• Stream speed = D − U2
• Time = distancespeed
• Distance = speed × time
• Equal-distance average speed = 2DUD + U
• Check units and identify exactly what is asked

Final exam tip: When downstream and upstream speeds are given, their sum and difference reveal the boat speed and stream speed directly.

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