## Boats and Streams

#### Boats and Streams

1. 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 ?

1. Let the speed in still water be x km/hr
Then, 6/x + 4 + 6/x - 4 = 2

##### Correct 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(x2 - 16)
⇒ x2 - 6x - 16 = 0
⇒ (x - 8) (x + 2) = 0
∴ x = 8 km/hr

1. 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 ?

1. Speed upstream = 6 km/hr
Speed downstream = 10 km/hr
∴ Speed of the current = (10 - 6)/2 km/hr = 2 km/hr

##### Correct Option: C

Speed upstream = 6 km/hr
Speed downstream = 10 km/hr
∴ Speed of the current = (10 - 6)/2 km/hr = 2 km/hr

1. A man rows upstream 16 km and downstream 28 km talking 5 hours each time. The velocity of the current is ?

1. Speed downstream = (28/5) km/hr = 5.6 km/hr
Speed upstream = (16/5) km/hr = 3.2 km/hr

##### Correct 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

1. 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 ?

1. 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

##### Correct 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

1. 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 ?

1. 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