Boats and Streams
 The current of a stream runs at the rate of 4 km/hr. A boat goes 6 km and back to the starting point in 2 hours. The speed of the boat in still water is ?

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Let the speed in still water be x km/hr
Then, 6/x + 4 + 6/x  4 = 2Correct Option: C
Let the speed in still water be x km/hr
Then, 6/x + 4 + 6/x  4 = 2
⇒ 6[ x  4 + x + 4] = 2(x^{2}  16)
⇒ x^{2}  6x  16 = 0
⇒ (x  8) (x + 2) = 0
∴ x = 8 km/hr
 A boat moves upstream at the rate of 1 km in 10 minutes and downstream at the rate of 1 km in 6 minutes. The speed of the current is ?

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Speed upstream = 6 km/hr
Speed downstream = 10 km/hr
∴ Speed of the current = (10  6)/2 km/hr = 2 km/hrCorrect Option: C
Speed upstream = 6 km/hr
Speed downstream = 10 km/hr
∴ Speed of the current = (10  6)/2 km/hr = 2 km/hr
 A man rows upstream 16 km and downstream 28 km talking 5 hours each time. The velocity of the current is ?

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Speed downstream = (28/5) km/hr = 5.6 km/hr
Speed upstream = (16/5) km/hr = 3.2 km/hrCorrect Option: B
Speed downstream = (28/5) km/hr = 5.6 km/hr
Speed upstream = (16/5) km/hr = 3.2 km/hr
Velocity of current = (5.6  3.2)/2 km/hr = 1.2 km/hr
 A man can row at 5 km/hr in still water and the velocity of current is 1 km/hr. It takes him 1 hour to row to a place and back. How far is the place ?

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Speed downstream = (5 + 1) km/hr = 6 km/hr
Speed upstream = (5  1) km/hr = 4 km/hr
Let the required distance be d km
Then, d/6 + d/4 = 1Correct Option: B
Speed downstream = (5 + 1) km/hr = 6 km/hr
Speed upstream = (5  1) km/hr = 4 km/hr
Let the required distance be d km
Then, d/6 + d/4 = 1
⇒ 2d + 3d = 12
∴ d = 2.4 km
 A man can row 44 km downstream in 4 hours. If the man's rowing rate in still water is 8 km/hr, then find in what time will he cover 25 km upstream ?

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Man's rate in still water = (man's rate with current + his rate against current)/2
Correct Option: A
∵ Man's rate in still water = (man's rate with current + his rate against current)/2
⇒ 8 = 1/2 [ 44/4 + 25/T ]
⇒ 16 = 11 + 25/T
∴ T = 5 hours