# Boats and Streams Solved Examples - Set 01

### Boats and Streams Problems with Detailed Solution

Question No: 01
A boat goes 16 km upstream in 2 hours and downstream in 1 hour. Find how time this boat will take to travel 32 km in all still water?
(A) 1.5 hours
(B) 2 hours
(C) 2 hours 40 minutes
(D) 2.5 hours
Solution:
Speed in upstream = 16/2 kmph = 8 kmph
Speed in downstream = 16 kmph
Speed of boat in still water = 1/2(Speed in upstream + Speed in downstream)
=1/2 (16 + 8) kmph
= 12 kmph
(Or),
x + y = 16/1 =16......... (eq. 1)
x - y = 16/1 = 8..........(eq. 2)
Adding equation (1) and equation (2), we get,
x=12 kmph
Therefore, time taken by the boat to travel 32 km is,
t = 32/12
= 2 hrs 40 min.

Question No: 02
A man goes by motor boat a certain distance upstream at 15 kmph and returns the same downstream at 20 kmph. The total time taken for the journey was 7 hrs. Find how far did he go?
(A) 30 km
(B) 60 km
(C) 90 km
(D) 120 km
Solution:
If the boat goes a certain distance ‘d’ downstream and returns upstream and total time                     taken be ‘t’, then t = {d/(x - y)} + {d/(x + y)} = = (d/upstream) + (d/downstream)
Therefore, 7 = (d/15) + (d/20)
=> d = 60 km.

Question No: 03
A man can row 5 km per hr in still water. If the river is flowing at 1 km per hr, it takes him 75 minutes to row to a place and back. How far is the place?
(A) 2.5 km
(B) 3 km
(C) 3.5 km
(D) 4.5 km
Solution:
If the boat goes a certain distance ‘d’ downstream and returns upstream and total time                       taken be ‘t’, then t = {d/(x - y)} + {d/(x + y)}
75 min = 75/60 hrs
Therefore, 75/60 = {d /(5 + 1)} + {d/ (5 - 1)}
=> 5/4 = (2d + 3d)/12
=> d = 3 km.

Question No. 04
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
(A) 2 : 1
(B) 3 : 2
(C) 8 : 3
(D) None of these
Solution:
Let the man's rate upstream be ‘x’ kmph and that downstream be ‘y’ kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
=> (x × 8 4/5) = (y × 4)
=> 44x/5 = 4y
=> y = 11x/5
∴ Required ratio = (y + x)/2 : (y - x)/2
= [(16x/5) × (1/2)] : [(6x/5) × (1/2)]
= 8/5 : 3/5
= 8 : 3

Question No. 05
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
(A) 4
(B) 5
(C) 6
(D) 10
Solution:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
∴ {30/(15 + x)} + {30/(15 - x)} = 4½
=> 900/(225 - x²) = 9/2
=> 9x2 = 225
=> x2 = 25
=> x = 5 km/hr.

Question No. 06
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
(A) 2 mph
(B) 2.5 mph
(C) 3 mph
(D) 4 mph
Solution:
Let the speed of the stream x mph. Then,
Speed downstream = (10 + x) mph,
Speed upstream = (10 - x) mph.
∴ {36/(10 - x)} - {36/(10 - x)} = 90/60
=> 72x x 60 = 90 (100 - x2)
=> x2 + 48x - 100 = 0
=> (x + 50)(x - 2) = 0
=> x = 2 mph.

Question No. 07
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(A) 2.4 km
(B) 2.5 km
(C) 3 km
(D) 3.6 km
Solution:
Speed downstream = (5 + 1) kmph = 6 kmph.
Speed upstream = (5 - 1) kmph = 4 kmph.
Let the required distance be x km.
Then, (x/6) + (x/4) = 1
=> 2x + 3x = 12
=>5x = 12
=> x = 2.4 km.

Question No. 08
A man can row three-quarters of a kilometer against the stream in 11¼ minutes and down the stream in 7½ minutes. The speed (in km/hr) of the man in still water is:
(A) 2
(B) 3
(C) 4
(D) 5
Solution:
We can write three-quarters of a kilometer as 750 meters, and 11¼ minutes as 675 seconds.
Rate upstream = (750/675) m/sec = (10/9) m/sec
Rate downstream = (750/450) m/sec = (5/3) m/sec
∴ Rate in still water = ½ {(10/9) + (5/3)} m/sec
= (25/18) m/sec
= {(25/18) × (18/5)} km/hr
= 5 km/hr

Question No. 09
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
(A) 2 : 1
(B) 3 : 1
(C) 3 : 2
(D) 4 : 3
Solution:
Let man's rate upstream be x kmph.
Then, his rate downstream = 2x kmph.
∴ (Speed in still water) : (Speed of stream) = {(2x + x)/2} : {(2x - x)/2}
= (3x/2) : (x/2)
= 3 : 1

Question No. 10
A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
(A) 1 km/hr
(B) 1.5 km/hr
(C) 2 km/hr
(D) 2.5 km/hr
Solution:
Suppose he move 4 km downstream in x hours. Then,
Speed downstream = (4/x) km/hr
Speed upstream = (3/x) km/hr
∴ {48/(4/x)} + {48/(3/x)} = 14 or x = ½
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = ½ (8 - 6) km/hr = 1 km/hr.

Boats and Streams:
Formula:                Boats and Streams Formulas
Solved Examples:  Solved Examples: Set 01
Practice Test:         Practice Test: 01