Boats and Streams
- In a river, the ratio of the speed of stream and speed of a boat in still water is 2 : 5 Again, ratio of the speed of stream and speed of an another boat in still water is 3 : 4. What is the ratio of the speeds of the first boat to the second boat in still water ?
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For the first boat,
Speed of stream : Speed of boat = 2: 5
Let speed of stream be 2x km/h and speed of boat = 5x km/h
Similarly, for the second boat
Speed of stream be 3y km/h and speed of boat = 4y
In both of the conditions, river is same.
∴ 2x = 3y
⇒ x = 3y/2
Thus, required ratio in speeds of boats in still water
= Thus, required ratio in speeds of boats in still water
= 5x : 4y = (5 x 3)y/2 : 4y = 15 : 8Correct Option: B
For the first boat,
Speed of stream : Speed of boat = 2: 5
Let speed of stream be 2x km/h and speed of boat = 5x km/h
Similarly, for the second boat
Speed of stream be 3y km/h and speed of boat = 4y
In both of the conditions, river is same.
∴ 2x = 3y
⇒ x = 3y/2
Thus, required ratio in speeds of boats in still water
= Thus, required ratio in speeds of boats in still water
= 5x : 4y = (5 x 3)y/2 : 4y = 15 : 8
- A steamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of the stream is 2 km/h, then find the distance between the two ports. ?
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Let the distance between the two ports be x km.
Then, speed downstream = x/4
And speed upstream = x/5
∴ Speed of the stream = [speed downstream + speed upstream] / 2 = (x/4 - x/5)/2Correct Option: D
Let the distance between the two ports be x km.
Then, speed downstream = x/4
And speed upstream = x/5
∴ Speed of the stream = [speed downstream + speed upstream] / 2 = (x/4 - x/5)/2
⇒ (5x -4x)/40 = 2
⇒ x/40 = 2
∴ x = 80 km
- A boat running upstream covers a distance of 10 km in 30 min and while running downstream, it covers the same distance in 25 min away and return, then the speed of the water current is ?
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Speed upstream = 10 / (30/60) = (10 x 60)/30 = 20 km/h
Speed downstream = 10/(25/60) = (10 x 60)/25 = 24 km/h
∴ Speed of the river's current = (24 - 20)/2Correct Option: C
Speed upstream = 10 / (30/60) = (10 x 60)/30 = 20 km/h
Speed downstream = 10/(25/60) = (10 x 60)/25 = 24 km/h
∴ Speed of the river's current = (24 - 20)/2 = 4/2 = 2 km/h
- A boat takes 9 h to travel a distance upstream and taken 3 h to travel the same distance downstream. If the speed of the boat in still water is 4 km/h, then what is the velocity of the stream ?
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Let velocity of the stream be x km/h
∴ Velocity of the boat downstream = (4 + x) km/h
and velocity of the boat upstream = (4 - x) km/h
According to the question, 3(4 + x) = 9(4 - x)Correct Option: D
Let velocity of the stream be x km/h
∴ Velocity of the boat downstream = (4 + x) km/h
and velocity of the boat upstream = (4 - x) km/h
According to the question, 3(4 + x) = 9(4 - x)
⇒ 12 + 3x = 36 - 9x
⇒ 12x = 24
∴ x = 2 km/h
- A boat's speed in still water is 5km/h. While river is flowing with a speed of 2km/h and time taken to cover a certain distance upstream is 2 h more than time taken to cover the same distance downstream. Find the distance ?
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Let the distance be D km.
Speed download = (5 +2) = 7 km/h
and speed upstream = (5 -2) = 3 km/h
According to the question,
D/3 - D/7 = 2Correct Option: A
Let the distance be D km.
Speed download = (5 +2) = 7 km/h
and speed upstream = (5 -2) = 3 km/h
According to the question,
D/3 - D/7 = 2
⇒ 7D - 3D = 21 x 2
∴ D = (21 x 2)/4 = 10.5 km
