Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Speed upstream = 7.5 kmph; Speed downstream = 10.5 kmph.
? total time taken = [105/7.5 + 105/10.5] hours = 24 hours.
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NA
SHSTTON
8
Solv. Corr.
7
Solv. In. Corr.
15
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13 / 24
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A man can row 7 kmph in still water. If in a river running at 1.5 km an hour, it takes him 50 minutes to row to a place and back, how far off is the place?
Speed downstream = (7.5 + 1.5) kmph = 9 kmph;
Speed upstream = (7.5 - 1.5) kmph = 6 kmph.
Let the required distance be x km. Then,
x/9 + x/6 = 50/60 ? 2x + 3x = [5/6 * 18] ? 5x = 15 ? x =3.
Hence, the required distance is 3 km.
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9
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A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Let's assume speed of the man in still water = x kmph
and the speed of the stream = y kmph.
As per the question Downstream + upstream
30/(x + y) + 20/(x - y) = 4 ------ (1)
45/(x + y) + 40/(x - y) = 7 ----- (2)
By Solving above equation the speed of man in still water = 12.5 kmph.
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3
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15
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A boat goes 100 km downstream in 10 hours, and 75 km upstream in 15 hours. The speed of the stream is?
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:
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.
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NA
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8
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4
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A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
river speed = 6 kmph
man can row in still water by speed = 1.2 kmph
man can row in downstream by speed = (6 + 1.2) kmph = 7.2 kmph
man can row in upstream by speed = (6 - 1.2) kmph = 4.8 kmph
Let's assume place distance form starting point = x km
So time taked for up and down = x/7.2 + x/4.8 = 1
=> x = 2.88 km
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NA
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7
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8
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A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.
Let x and y be the upstream and downstream speed respectively.
Hence 50/x + 72/y = 9 and 70/x + 90/y = 12
Solving for x and y we get x = 10 km/hr and y = 18 km/hr
Speed of the stream = 1/2 * (downstream speed - upstream speed)
= 1/2 (18 - 10) = 4 km/hr.
Workspace
NA
SHSTTON
10
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17
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27
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A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 20 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
man row 5 km in 60 min (1hr)
=> 5=(u+v)*1 ---------(1)
Further 20 km in 10 hrs.
=> 20=(u-v)*10 -------(2)
By solving eq. (1) & (2)
u=7/2
v=3/2
Therfore,
=> 20=(u+v)*t
=> 20=(3/2 + 7/2)*t => t=4hr
Hence, time saved = 6 hr.
Workspace
NA
SHSTTON
6
Solv. Corr.
12
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18
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20 / 24
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A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
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