Boats and Streams

Question:
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

Answer: Option A

Explanation:

Suppose he move 4 km downstream in x hours. Then,

Speed downstream =		4		km/hr.
		x

Speed upstream =		3		km/hr.
		x

	48	+	48	= 14 or x =	1	.
	(4/x)		(3/x)		2

So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

Rate of the stream =	1	(8 – 6) km/hr = 1 km/hr.
	2

Question: 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

Answer: Option A

Explanation:

Let the speed of the stream x mph. Then,

Speed downstream = (10 + x) mph,

Speed upstream = (10 – x) mph.

	36	–	36	=	90
	(10 – x)		(10 + x)		60

72x x 60 = 90 (100 – x2)

x2 + 48x – 100 = 0

(x+ 50)(x – 2) = 0

x = 2 mph.

Question: 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

Answer: Option B

Explanation:

Let the speed of the stream be x km/hr. Then,

Speed downstream = (15 + x) km/hr,

Speed upstream = (15 – x) km/hr.

	30	+	30	= 4	1
	(15 + x)		(15 – x)		2

	900	=	9
	225 – x2		2

9×2 = 225

x2 = 25

x = 5 km/hr.

Video Explanation: https://youtu.be/lMFnNB3YQOo

Question:
A boat covers a certain distance downstream in 1 hour, while it comes back in 1 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

[A].

12 kmph

[B].

13 kmph

[C].

14 kmph

[D].

15 kmph

Answer: Option D

Explanation:

Let the speed of the boat in still water be x kmph. Then,

Speed downstream = (x + 3) kmph,

Speed upstream = (x – 3) kmph.

(x + 3) x 1 = (x – 3) x	3
	2

2x + 6 = 3x – 9

x = 15 kmph.

Question:
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

Answer: Option A

Explanation:

Speed downstream = (5 + 1) kmph = 6 kmph.

Speed upstream = (5 – 1) kmph = 4 kmph.

Let the required distance be x km.

Then,	x	+	x	= 1
	6		4

2x + 3x = 12

5x = 12

x = 2.4 km.

Question:
Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

[A].

16 hours

[B].

18 hours

[C].

20 hours

[D].

24 hours

Answer: Option D

Explanation:

Speed upstream = 7.5 kmph.

Speed downstream = 10.5 kmph.

Total time taken =		105	+	105	hours = 24 hours.
		7.5		10.5

Question: The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
[A].

1.2 km

[B].

1.8 km

[C].

2.4 km

[D].

3.6 km

Answer: Option D

Explanation:

Speed downstream = (15 + 3) kmph = 18 kmph.

Distance travelled =		18 x	12	km = 3.6 km.
			60

Video Explanation: https://youtu.be/IDOwWUeOldQ

Question:
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

[A].

2 hours

[B].

3 hours

[C].

4 hours

[D].

5 hours

Answer: Option C

Explanation:

Speed downstream = (13 + 4) km/hr = 17 km/hr.

Time taken to travel 68 km downstream =		68	hrs = 4 hrs.
		17

Question:
A man’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man’s speed against the current is:

[A].

8.5 km/hr

[B].

9 km/hr

[C].

10 km/hr

[D].

12.5 km/hr

Answer: Option C

Explanation:

Man’s rate in still water = (15 – 2.5) km/hr = 12.5 km/hr.

Man’s rate against the current = (12.5 – 2.5) km/hr = 10 km/hr.

Question:
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].

Cannot be determined

Answer: Option C

Explanation:

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 x 8	4		= (y x 4)
			5

	44	x =4y
	5

y =	11	x.
	5

Required ratio =		y + x		:		y – x
		2				2

=		16x	x	1		:		6x	x	1
		5		2				5		2

=	8	:	3
	5		5

   = 8 : 3.