Boats and Streams
- A river is flowing at a speed of 5 km/h in a particular direction. A man, who can swim at a speed of 20 km/h in still water, starts swimming along the direction of flow of the river from from points A and reaches another point B which is at a distance of 30 km from the starting point A. On reaching point B, the man turns back and starts swimming against the direction of flow of the river and stops after reaching point A. The total time taken by the man to complete his journey is ?
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Given,
Speed of the stream = 5 km/h
and speed of the man in still water = 20 km/h
∴ Speed of the man downstream = 20 + 5 = 25 km/h
and speed of the man upstream = 20 - 5 = 15 km/h
∴ Total time taken to complete the whole journey = 30/25 + 30/15Correct Option: B
Given,
Speed of the stream = 5 km/h
and speed of the man in still water = 20 km/h
∴ Speed of the man downstream = 20 + 5 = 25 km/h
and speed of the man upstream = 20 - 5 = 15 km/h
∴ Total time taken to complete the whole journey = 30/25 + 30/15
= (30 x 8) / 75
= 3 h 12 min
- The ratio of speed of a motorboat to that of the current of water is 35 : 5. The motorboat goes along with the current in 5 h 10 min. Find the time to come back of motorboat ?
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Let speed of a motorboat be = 36k km/h
and speed of the current = 5k km/h
∴ Speed downstream = (36 + 5)k = 41k km/h
and speed upstream = (36 - 5)k = 31k km/hCorrect Option: C
Let speed of a motorboat be = 36k km/h
and speed of the current = 5k km/h
∴ Speed downstream = (36 + 5)k = 41k km/h
and speed upstream = (36 - 5)k = 31k km/h
Let distance be D km.
According to the question
When boat goes along with the current.
Distance = Time x Speed
⇒ D = (5 + 10/60) x 41k
⇒ D = 31/6 x 41k ....(i)
Again, when boat come back
a = Time x Speed
From Eq. (i) .
31/6 x 41k = Time x 31k
⇒ Time = 41/6
Time = 6 h 50 min.
- A man can row 71/2 km/h in still water. If in a river running at 1.5 km/h, it takes him 50 min to row to a place and back, how far off is the place ?
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Let the distance be L km.
Speed of the main in still water = 71/2 km/h
and speed of the river = 15 km/h
∴ Speed of the man downstream = 7.5 + 1.5 = 9
Speed of the man upstream = 7.5 - 1.5 = 6 km/h
According to the question,
L/9 + L/6 = 50/60Correct Option: A
Let the distance be L km.
Speed of the main in still water = 71/2 km/h
and speed of the river = 15 km/h
∴ Speed of the man downstream = 7.5 + 1.5 = 9
Speed of the man upstream = 7.5 - 1.5 = 6 km/h
According to the question,
L/9 + L/6 = 50/60
⇒ (4L + 6L)/36 = 50/60
⇒ 10L/36 = 50/60
⇒ L = (50 x 36)/(10 x 60)
5⇒ x = 3 km
- Ishwar is rowing a boat. He takes half time in moving a certain distance downstream than upstream. What is the ratio of the rate of boat in still water to the rate of current ?
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Let speed of Ishwar's boat in still water be x km/h
and speed of current = y km/h
Rate downstream = (x + y) km/h
Rate upstream = (x - y) km/h
Let the distance covered in each case be a.
According to the question,
2a/(x + y) = a/(x - y)Correct Option: D
Let speed of Ishwar's boat in still water be x km/h
and speed of current = y km/h
Rate downstream = (x + y) km/h
Rate upstream = (x - y) km/h
Let the distance covered in each case be a.
According to the question,
2a/(x + y) = a/(x - y)
⇒ 2(x - y) = x + y
2x - 2y = x + y
⇒ x = 3y
∴ x/y = 3/1
⇒ x : y = 3 : 1
- A boatman takes twice as long to row a distance against the stream as to row the same distance with the stream. Find the ratio of speeds of the boat in still water and the stream. ?
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Let boatman's speed upstream x
And his speed downstream = 2x
∴ Ratio = (Speed in still water) : (Speed of stream)Correct Option: B
Let boatman's speed upstream x
And his speed downstream = 2x
∴ Ratio = (Speed in still water) : (Speed of stream)
= (2x + x/2) : (2x - x/2)
= 3x/2 : x/2
= 3 : 1
