Boats and Streams is an application of the problems based on Time, Speed and Distance. In this topic, you will learn how to solve problems using the concept of relative speed. We have given some formulae along with solved question and answers that will help you in solving these problems. Once you complete this topic you must be able to solve problems based on stream speed, boat speed or a man rowing in a stream, time taken to to row etc using the formulae explained in this section.
Boats and Streams
1. Downstream: If a boat is travelling in the direction of the stream, the boat is said to be travelling downstream.
2. Upstream: If a boat is travelling opposite to the direction of the stream, the boat is said to be travelling upstream.
3. If the speed of the boat is $u$ km/hr and speed of the stream is $v$ km/hr, then
Speed Downstream(D) = $u\text{ }+\text{ }v$ km/hr
Speed Upstream(U) = $u\text{ }-\text{ }v$ km/hr
4. If speed downstream(D km/hr) and speed upstream(U km/hr) is given, then
Speed of the boat in still water(u) = $\frac{D\text{ }+\text{ }U}{2}$ km/hr
Rate of the stream(v) = $\frac{D\text{ }-\text{ }U}{2}$ km/hr
Problems
Boats and Streams - Exercise - Blog
14 questions
- If a boat can row downstream at 6 km/hr & upstream at 4 km/hr. Find the speed of boat in still water.
- 10 km/hr
- 5 km/hr
- 6 km/hr
- 12 km/hr
Show the answer
Answer: 5 km/hr
Speed downstream, v = 6 km/hr
Speed upstream, u = 4 km/hr
Speed of the boat in still water = $\frac12$ (v+u)
$\frac12$ (6 + 4) = 5 km/hr
- If a man rows 500m in 6 minutes & returns back in 10 minutes. Find the speed of the stream.
- 1.5 m/s
- 2 m/s
- 1 m/s
- 0.5 m/s
Show the answer
Answer: 1 m/s
Speed downstream, v = $\frac{500 }{6 \text{x} 60}$ x $\frac{18}{5}$ = 5 m/s
Speed upstream, u = $\frac{500}{10 \text{x} 60}$ x $\frac{18}{5}$ = 3 m/s
Speed of the stream = $\frac12 (v-u)$ = $\frac12 (5-3)$ = 1 m/s
- If a man can row 10 km downstream in 50 minutes. If speed of the boat is 8 km/hr. Find the speed of the stream.
- 4 km/hr
- 6 km/hr
- 8 km/hr
- 10 km/hr
Show the answer
Answer: 4 km/hr
Speed downstream, v = $\frac{10}{\frac{50}{60}}$ km/hr = 12 km/hr
Speed of the boat, b = 8 km/hr.
Speed of stream, s = ?
Speed downstream = Speed of the boat + Speed of the stream
12 km/hr = 8 km/hr + s
s = 4 km/hr
- A boat takes 5 hours to row a certain distance downstream and reach back to its starting point upstream. If the speed of the boat is 5 km/hr and stream is 1 km/hr. Find the total distance travelled by boat.
- 6 hours
- 8 hours
- 10 hours
- 12 hours
Show the answer
Answer: 12 hours
Speed of the boat, b = 5 km/hr
Speed of the stream, s = 1 km/hr
Speed downstream, v = b+s = 6 km/hr
Speed upstream, u = b - s = 4 km/hr
Let the distance travelled upstream and downstream be 2D.
The time taken to travel downstream = $\frac{\text{Distance downstream}}{\text{Speed downstream}} =\frac{D}{6}$
The time taken to travel upstream = $\frac{\text{Distance upstream}}{\text{Speed upstream}} =\frac{D}{4}$
$\frac D6 +\frac D4$ = Total time to travel downstream and upstream
$\frac D6 +\frac D4$ = 5
10D = 120
D = 12 hours.
- Speed of boat is 6 km/hr and speed of stream is 2 km/hr. If the boat rows a distance of 12 kms downstream and returns back.. Find the total time taken by the boat.
- 12 hrs
- 9 hrs
- 4.5 hrs
- 6 hrs
Show the answer
Answer: 4.5 hrs
Boat speed, b = 6 km/hr
Stream speed, s = 2 km/hr
Speed upstream, u = 6 - 2 = 4 km/hr
Speed downstream, v = 6 + 2 = 8 km/hr
Distance, D = 12 kms
Total time taken to row downstream and upstream =
$\frac {\text{Distance downstream}}{\text{Speed downstream}} +\frac{\text{Distance upstream}} {\text{Speed upstream}}$
= $\frac{12}{8} + \frac{12}{4}$
= 4.5 hrs
- If a man takes double the time to row upstream than rowing the same distance downstream, find the ratio of the speeds of the man and stream.
- 2 : 3
- 3 : 2
- 1 : 3
- 3 : 1
Show the answer
Answer: 3 : 1
Man speed, m
Stream speed, s
Speed upstream, u = m - s
Speed downstream, v = m + s
Time taken to row upstream = 2 x Time taken to row downstream
$\frac{\text{Distance upstream}}{\text{Speed upstream}}$ = 2 x$\frac{\text{Distance downstream}}{\text{Speed downstream}}$
$\frac Du$ = 2 x $\frac D v$
$\frac{D}{b-s}$ = 2 x $\frac{D}{b+s}$
m + s = 2 (m - s)
m = 3s
m : s = 3 : 1
Ratio of speed of the man to the stream = 3 : 1
- A boat can row a distance of 2 kms downstream in 5hrs. If the speed of stream is 1 km/hr. Find the time taken by the boat to travel upstream.
- 8 hrs
- 5 hrs
- 10 hrs
- 12 hrs
Show the answer
Answer: 10 hrs
Boat speed, b
Stream speed, s = 1 km/hr
Speed upstream, u = b - 1
Speed downstream, v = b + 1
Distance downstream = 5 kms
Time taken to row downstream = 2 hrs
Time taken to row upstream = ?
v => b + 1 = $\frac{\text{Distance downstream}}{\text{Time taken to row downstream}} =\frac52$ = 2.5 km/hr
b + 1 = 2.5 km/hr
b = 1.5 km/hr
Time taken to row upstream = $\frac{\text{Distance upstream}}{\text{speed upstream}}$
= $\frac{5}{1.5-1}$
= 10 hrs
- A boat rows to a place 40 kms away and reaches back to the starting point in 15 hrs. If the boat rows 8 kms downstream in the same time as 4 kms upstream. Find the speed of the stream.
- 1 km/hr
- 1.25 km/hr
- 2.25 km/hr
- 2 km/hr
Show the answer
Answer: 2.25 km/hr
Boat speed, b
Stream speed, s
Speed upstream, u = b - s
Speed downstream, v = b + s
Distance downstream = 40 kms
Distance upstream = 40 kms
Time taken to row downstream and then upstream = 15 hrs
Time taken to row upstream = ?
Total time to travel downstream and upstream = $\frac{D}{b + s} + \frac{D}{b - s}$
15 =$\frac{45}{b+s} + \frac{45}{b-s}$
1 = $\frac{3}{b+s} +\frac{3}{b-s}$ …………. A
Since the man rows 8 kms downstream in the same time as 4 kms upstream
$\frac{8}{b+s} = \frac{4}{b-s}$
solving we get, b = 3s
Substituting b = 3s in A above,
1 = $\frac{3}{4s} + \frac{3}{2s}$
s = 2.25 km/hr.
Speed of the stream = 2.25 km/hr
- A man can row at a speed of 4 km/hr in still water. His speed upstream is 2.5 km/hr. Find his speed downstream.
- 5.5 km/hr
- 5 km/hr
- 6.5 km/hr
- 6 km/hr
Show the answer
Answer: 5.5 km/hr
Man speed, m = 4 km/hr
Stream speed, s
Speed upstream, m - s = 2.5
4 - s = 2.5
s = 1.5 km/hr
Speed downstream = m + s = 4 + 1.5 = 5.5 km/hr
- A boat running downstream covers a distance of 24 kms in 4 hrs, while for covering the same distance upstream if takes 6 hrs. Find the speed of boat in still water.
- 5 km/hr
- 7 km/hr
- 9 km/hr
- 12 km/hr
Show the answer
Answer: 5 km/hr
Distance downstream = 24 kms
Time downstream = 4 hrs
Distance upstream = 24 kms
Time upstream = 6 hrs
Boat speed, b = ?
Speed downstream, v = $\frac{\text{Distance downstream}}{\text{Time downstream}} = \frac{24}{4}$ = 6 km/hr
Speed upstream, u = $\frac{\text{Distance upstream}}{\text{Time upstream}} = \frac{24}{6}$ = 4 km/hr
Boat speed = $\frac12 (u + v) =\frac12$ (6 + 4) = 5 km/hr
- If a man covers certain distance downstream in 3 hrs and returns back in 3 hrs. If the speed of the stream is 2 km/hr. What is the speed of boat in still water?
- 7.5 km/hr
- 10 km/hr
- 5 km/hr
- 12 km/hr
Show the answer
Answer: 10 km/hr
Time downstream = 2 hrs
Time upstream = 3 hrs
Stream speed, s = 2 km/hr
Boat speed, b = ?
Since distance is constant,
Speed upstream x Time upstream = Speed downstream x Time downstream
(b - s) x 3 = (b + s) x 2
(b - 2) x 3 = (b + 2) x 2
3b - 6 = 2b + 4
b = 10 km/hr
Hence speed of the boat in still water = 10 km/hr
- If the speed of a boat in still water is 6 km/hr and the speed of the stream is 2 km/hr. Find the ratio of time taken by the boat to travel the same distance upstream and downstream.
- 1 : 2
- 2 : 1
- 3 : 4
- 4 : 3
Show the answer
Answer: 1 : 2
Boat speed = 6 km/hr
Stream speed = 2 km/hr
Speed upstream = 6 - 2 = 4 km/hr
Speed downstream = 6 + 2 = 8 km/hr
Since distance is constant. Time is inversely proportional to speed.
$\frac{\text{Time upstream}}{\text{Time downstream}} = \frac{\text{Speed downstream}}{\text{Speed upstream}}$
= $\frac{4}{8} = \frac12$
Ratio of time taken by the boat to travel the same distance upstream and downstream is 1 : 2
- A man rows 20 kms downstream and 8 kms upstream taking 2 hrs each time. What is the speed of the boat?
- 10 km/hr
- 4 km/hr
- 7 km/hr
- 12 km/hr
Show the answer
Answer: 7 km/hr
Speed downstream, v = $\frac{20}{2}$ = 10 km/hr
Speed upstream, u = $\frac82$ = 4 km/hr
Speed of the boat = $\frac12$(10 + 4) = 7 km/hr
- If a man rows a distance of 12 kms downstream in 2 hrs and 10 kms upstream in 2.5 hrs. Find the total time taken by the man to row a stretch of 20 kms upstream and downstream.
- 4 hrs
- 7 hrs
- 9 hrs
- 12 hrs
Show the answer
Answer: 12 hrs
Speed downstream = $\frac{12}{2}$ = 6 km/hr
Speed upstream = $\frac{10}{2.5}$ = 4 km/hr
Total time to row a stretch of 20 kms upstream and downstream =
$\frac{20}{10} + \frac{20}{2}$ = 12 hrs
