Boats and Streams
- Ashutosh can row 24 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream. ?
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Let rate of stream be 'a' km/h.
According to the question.
24 + a = 2(24 - a)Correct Option: C
Let rate of stream be 'a' km/h.
According to the question.
24 + a = 2(24 - a)
⇒ 24 + a = 48 - 2a
⇒ 3a = 48 - 24 = 24
∴ a = 24/3 = 8 km/h
- A boat goes 12 km in 1 h in still water. It takes thrice time in covering the same distance against the current. Find the speed of the current. ?
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Speed of a boat in still water = distance / time = 12/1 = 12 km/h
Speed against the current = 12/3 km/h
Let the speed of the current = x km/h
According to the question,
12 - x = 4Correct Option: A
Speed of a boat in still water = distance / time = 12/1 = 12 km/h
Speed against the current = 12/3 km/h
Let the speed of the current = x km/h
According to the question,
12 - x = 4
⇒ x = 8 km/h
- 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
- A river is flowing with a steady speed of 4 km/h. One rows his boat downstream in the river and then returns by rowing upstream in the same river. When he returns to the starting points, the total distance covered by him is 42 km. If the return journey takes 2 h more than his outward journey, then the speed of his rowing in still water must be ?
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Let the speed of rowing in still water be u km/h.
Distance in downstream motion = 21 km
and speed downstream = (u + 4) km/h
∴ Time taken = 21/ (u + 4)
Distance upstream motion = 21 km and speed upstream = (u +4) km
∴ Time taken = 21/(u - 4)
According to the question.
21/(u + 4) + 2 = 21/(u - 4)Correct Option: B
Let the speed of rowing in still water be u km/h.
Distance in downstream motion = 21 km
and speed downstream = (u + 4) km/h
∴ Time taken = 21/ (u + 4)
Distance upstream motion = 21 km and speed upstream = (u +4) km
∴ Time taken = 21/(u - 4)
According to the question.
21/(u + 4) + 2 = 21/(u - 4)
⇒ (21 + 2u + 8)/u + 4 = 21/(u - 4)
⇒ (2u + 29)/(u + 4) = 21/(u - 4)
⇒ (u - 4) (2u + 29) = 21(u + 4)
⇒ 2u2 - 8u + 29u - 116 = 21u + 84
⇒ 2u2 + 21u - 116 = 21u + 84
⇒ 2u2 = 84 + 116
⇒ u2 = 200/2
⇒ u2 = 100
⇒ u = 10 km/h
- 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