A boat goes 20 km downstream in 2 hours and 12 km upstream in 2 hours. What is the speed of the boat in still water?

8 km/h. Downstream speed = 202 = 10 km/h, upstream = 122 = 6 km/h. Boat speed = 10 + 62 = 8 km/h.

For the boat that goes 10 km/h downstream and 6 km/h upstream, what is the speed of the stream?

2 km/h. Stream speed = 10 - 62 = 2 km/h.

A man rows at 6 km/h in still water. The river flows at 2 km/h. How long will he take to row 24 km downstream?

3 h. Downstream speed = 6 + 2 = 8 km/h, so the time is 248 = 3 hours.

A boat's speed in still water is 15 km/h and the stream flows at 5 km/h. If a round trip to a point and back takes 1 hour, how far is the point?

203 km. d20 + d10 = 1, i.e. 3d20 = 1, so d = 203 km 6.67 km.

A boat takes twice as long to row a certain distance upstream as it does downstream. If the boat's speed in still water is 12 km/h, what is the speed of the stream?

4 km/h. Twice the time upstream means the downstream speed is twice the upstream speed: 12 + s = 2(12 - s), so 3s = 12 and s = 4 km/h.

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Quantitative Aptitude · Time, Work & Distance

Boats and Streams — Questions & Answers

The current adds to the boat's still-water speed when going downstream and subtracts when going upstream. Two measurements let you recover both the boat speed and the stream speed.

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Key formulas

Downstream speed $= b + s$ ; upstream speed $= b - s$
$b = \dfrac{(\text{down}) + (\text{up})}{2}$ ; $\;s = \dfrac{(\text{down}) - (\text{up})}{2}$
If the same distance $d$ each way: total time $= \dfrac{d}{b+s} + \dfrac{d}{b-s}$

5 solved Boats and Streams questions

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01
A boat goes 20 km downstream in 2 hours and 12 km upstream in 2 hours. What is the speed of the boat in still water?
4 steps · reveal one at a time
1. Step 1: Find Downstream Speed
  First, let's find the downstream speed. The boat goes $20 \text{ km}$ in $2 \text{ hours}$ . Using the formula Speed $=$ Distance $/$ Time, the downstream speed is $20 \text{ km} / 2 \text{ hours} = 10 \text{ km/h}$ . This is the boat's speed plus the current's speed.
2. Step 2: Find Upstream Speed
  Next, let's find the upstream speed. The boat goes $12 \text{ km}$ in $2 \text{ hours}$ . Using the same formula, the upstream speed is $12 \text{ km} / 2 \text{ hours} = 6 \text{ km/h}$ . This is the boat's speed minus the current's speed.
3. Step 3: Calculate Boat Speed
  The speed of the boat in still water is the average of its downstream and upstream speeds. We can calculate it using the formula: Boat Speed $=$ (Downstream Speed $+$ Upstream Speed) $/ 2$ . This cancels out the effect of the current.
4. Step 4: The answer
  So the answer is (C) 8 km/h. Plugging in our values: Boat Speed $=$ ( $10 \text{ km/h} + 6 \text{ km/h}$ ) $/ 2 = 16 \text{ km/h} / 2 = 8 \text{ km/h}$ . This is the boat's true speed without the current.
02
For the boat that goes 10 km/h downstream and 6 km/h upstream, what is the speed of the stream?
4 steps · reveal one at a time
1. Step 1: Identify the speeds
  We are given the boat's speed when going downstream (with the current) as $10$ km/h, and its speed when going upstream (against the current) as $6$ km/h.
2. Step 2: Recall the formula
  To find the speed of the stream, you can use the formula: Stream speed $= \frac{\text{Downstream speed} - \text{Upstream speed}}{2}$ .
3. Step 3: Calculate stream speed
  Now, substitute the given values into the formula: Stream speed $= \frac{10 - 6}{2} = \frac{4}{2} = 2$ km/h.
4. Step 4: The answer
  So the answer is (B) 2 km/h. This calculation directly gives us the speed of the water current.
03
A man rows at 6 km/h in still water. The river flows at 2 km/h. How long will he take to row 24 km downstream?
4 steps · reveal one at a time
1. Step 1: Identify given speeds
  We are given the man's speed in still water as $6$ km/h and the river's current speed as $2$ km/h. He needs to row a total distance of $24$ km.
2. Step 2: Find downstream speed
  When rowing downstream, the river's current helps the man, so their speeds add up. The effective downstream speed is $6 + 2 = 8$ km/h.
3. Step 3: Calculate total time
  To find the time taken, we use the formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$ . We have a distance of $24$ km and a downstream speed of $8$ km/h.
4. Step 4: The answer
  So the answer is (C) 3 h because $24 \text{ km} \div 8 \text{ km/h} = 3 \text{ hours}$ .
04
A boat's speed in still water is 15 km/h and the stream flows at 5 km/h. If a round trip to a point and back takes 1 hour, how far is the point?
5 steps · reveal one at a time
1. Step 1: Calculate boat speeds
  First, find the boat's speed with the stream (downstream) and against the stream (upstream). The downstream speed is $15 + 5 = 20 \text{ km/h}$ . The upstream speed is $15 - 5 = 10 \text{ km/h}$ .
2. Step 2: Set up time equations
  Let $d$ be the distance to the point. The time taken to travel downstream is $\frac{d}{20}$ hours. The time taken to travel upstream is $\frac{d}{10}$ hours. Remember, time equals distance divided by speed.
3. Step 3: Formulate total time
  The problem states the round trip takes 1 hour. So, the total time is the sum of the downstream and upstream travel times. This gives us the equation: $\frac{d}{20} + \frac{d}{10} = 1$ .
4. Step 4: Solve for distance
  To solve for $d$ , find a common denominator for the fractions, which is 20. The equation becomes $\frac{d}{20} + \frac{2d}{20} = 1$ . Combining these, we get $\frac{3d}{20} = 1$ . Multiplying both sides by 20 gives $3d = 20$ , so $d = \frac{20}{3}$ km.
5. Step 5: The answer
  So the answer is (B) $\dfrac{20}{3}$ km, as this is the distance calculated for one way of the round trip.
05
A boat takes twice as long to row a certain distance upstream as it does downstream. If the boat's speed in still water is 12 km/h, what is the speed of the stream?
5 steps · reveal one at a time
1. Step 1: Understand Time Ratio
  The problem tells us the boat takes twice as long to go upstream as it does downstream. For a constant distance, if time is doubled, speed must be halved. So, the downstream speed is twice the upstream speed.
2. Step 2: Define Speeds
  Let the boat's speed in still water be $B = 12$ km/h and the stream's speed be $s$ . The speed upstream is $B - s = 12 - s$ . The speed downstream is $B + s = 12 + s$ .
3. Step 3: Formulate Equation
  Using our understanding that downstream speed is twice the upstream speed, we can write the equation: $12 + s = 2(12 - s)$ . This equation connects all the given information.
4. Step 4: Solve for Stream Speed
  Now, let's solve the equation: $12 + s = 24 - 2s$ . Rearranging the terms gives $s + 2s = 24 - 12$ , which simplifies to $3s = 12$ . Dividing by 3, we find $s = 4$ km/h.
5. Step 5: The answer
  So the answer is (D) 4 km/h. This is the speed of the stream that satisfies the condition that the upstream journey takes twice as long.

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