Boats and Streams
Let us know what is Downstream and what is Upstream. Because these concepts are the heart of Boats and Streams.
Downstream : In water,the direction along the stream is called downstream. I mean, If a boat or a swimmer swims in the same direction as the stream, then it is called downstream. Obviously the boat or swimmer require less efforts to travel using downstream. Because the stream itself helps the objects to move.
Remember, as the object moves along with the water, the stream helps the object.
So, the down stream speed (DS) is
DS = U+V
where U is the speed of the object in the still (calm) water
V is the speed of the water.
Upstream : If the boat or the swimmer is swimming in the opposite direction in which the stream is passing is called upstream. In simple words, the direction against the stream is called upstream.
Remember, as the object moves against the water pushes the object in opposite direction.
So, the upstream speed (US) is
US = U-V
where U is the speed of the object in the still (calm) water
V is the speed of the water.
Important Formulas on Boats and Streams :
Let us assume that the speed of the boat in still water is U km/hr and the speed of stream is V km/hr then, as mentioned above :
Speed downstream = (u+v)km/hr
Speed upstream = (u-v)km/hr
èIf the speed downstream is a km/hr and the speed upstream is b km/hr then :
Speed in still water = 1/2(a+b) km/hr
Rate of stream = 1/2(a-b)km/hr
Questions : -
1. A boat can run 13 km/hr in still water and the speed of current 4 km/hr. in how many hours the boat will covered 68 km down streams?
(1) 2 hours (2) 3 hours
(3) 4 hours (4) 5 hours
2. A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the Velocity (in km/h) of current is:
(1) 1/2 (2) 3/2
(3) 2 (4) 5/2
3. A man can row at 5 km/h 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?
(1) 1.5 km (2) 2.4 km
(3) 3.5 km (4) 1 km
4. A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current.
(1) 5 (2) 3
(3) 6 (4) 4
5. In a stream running at 2 km/h, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.
(1) 22 km/hr (2) 20 km/hr
(3) 25 km/hr (4) 18 km/hr
6. A man takes 3 hours 45 minutes to row a boat I5 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the river current in km/hr.
(1) 1 km/hr (2) 2 km/hr
(3) 3 km/hr (4) 4 km/hr
7. A person can row a boat d km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream?
(1) 3/2 hours (2) 7 hours
(3) 7 (¼) (4) 7/2 hours
8. A man swimming in a stream which flows 1.5 km/h, finds that in a given time he can swim twice as fast with the stream as he can against it. At what rate does he swim?
(1) 4 km/hr (2) 4.5 km/hr
(3) 6 km/hr (4) 7 km/hr
9. A motorboat in still water travels at a sped of 36 km/h. It goes 56 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:
(1) 2 hours 25 minutes (2) 3 hours
(3) 1 hour 24 minutes (4) 2 hours 21 minutes
10. A man can row 6 km/h in still water. If the speed of the current is 2 km/h, it takes 3 hours more in upstream than in the downstream for the same distance.
(1) 30 km (2) 24 km
(3) 20 km (4) 32 km
ANSWER WITH EXPLANATION:
1. (3)
The speed downstream = 13+4 = 17 km/hr
∴Time taken to covered 68 km = 68/17 = 4 hours
2. (2)
Rate downstream = 32/6 km/h; Rate upstream = 14/6 km/h
Velocity of current = 1/2 (32/6 - 14/6) km/h
= 3/2 km/h
3. (2)
-Speed downstream = (5 + 1) km/h = 6 km/h.
Speed upstream = (5 – 1) km/h = 4 km/h.
Let the required distance be x km.
Then, x/6 + x/4 = 1
2x + 3x = 12
5x = 12
x = 2.4 km.
4. (2)
Let rate upstream = x km / hr and rate downstream = y km / hr.
Then, 40/x+ 55/y =13 ...(i)
and 30/x+44/y=10 ...(ii)
Multiplying (ii) by 4 and (i) by 3 and subtracting, we get :
11/y=1 or y=11.
Substituting y = 11 in (j), we get : x = 5.
\threrefore Rate in still water =1/2(11+5) km/h=8km/h.
\threrefore Rate in still water =1/2(11+5) km/h=8km/h.
Rateofcurrent = 1/2(11−5) km/h=3km/h.
5. (1)
Let the speed of the motorboat in still water be x km/h. Then,
Speed downstream = (x + 2) km/h; Speed upstream = (x - 2) km/h.
6/x+2+6/x−2 = 33/60
Speed downstream = (x + 2) km/h; Speed upstream = (x - 2) km/h.
6/x+2+6/x−2 = 33/60
<=> 11x2−242x+2x−44=0
«=> (x - 22) (11x + 2) = 0 <=> x = 22. Hence, speed of motorboat in still water = 22 km/h.
6. (1)
Rate downstream=15334 km/hr
Rate downstream=15334 km/hr
=15×415km/hr=4km/hr.
Rate upstream=(5212) km/hr
=(5×25)=2km/hr
Speed of current=12(4−2)km/hr=1km/hr.
7. (4)
Let the speeds of boat and stream be x and y km/hr respectively.
Then, Rate downstream = (x + y) km/hr and Rate upstream = (x - y) km/hr
Given d / (x+y) + d / ( x-y ) =5 hrs 15 minutes = 21/4 hours
and 2d / (x+y) = 7 => d / (x+y)=7/4 => 2d / (x+y)=7/2
Hence, he takes 7/2 hours to row 2d km distance downstream.
8. (2)
Rate of stream =1.5 km/hr
Let speed of man in still water = x km/hr and Distance = d
Upstream speed = (x - 1.5) km/hr Downstream speed = (x + 1.5) km/hr
Given, 2d / (x+1.5) = d/ (x-1.5) => 2x - 3 = x + 1.5 => x = 4.5 km/hr
9. (3)
Speed of the motorboat upstream
= 56km/1 ¾ hours
=32 km/h
Let the speed of the current = x km/h
36 – x = 32
à 36 – 32 = 4 km/h
speed of motorboat downstream = 36 + 4 = 40 km/h
Time taken to cover 56 km at 40 km/h = 56/40 = 7/5 hours
= 1 hour 24 minutes
10. (2)
Let he required distance be x km.
x/6-2 + x/ 6 + 2 = 3
à x/4 – x/8 = 3
à 2x –x/8 = 3
= x=3 x 8 = 24 km.
Give your answer in the comment section along with your timing and judge where you stand in the competition.
