## Boats and Streams

#### Boats and Streams

1. A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9km/hr and the speed of the current is 3 km/hr the distance between A and B is ?

1. Speed downstream = (9 + 3) km/hr = 12km/hr
Speed upstream = = (9 - 3) km/hr = 6km/hr
Let the distance AB = d km
Then, d/6 + d/12 = 3

##### Correct Option: D

Speed downstream = (9 + 3) km/hr = 12km/hr
Speed upstream = = (9 - 3) km/hr = 6km/hr
Let the distance AB = d km
Then, d/6 + d/12 = 3
⇒ 2d + d = 36
⇒ d = 12
∴ Distance AB = 12 km

1. A man can swim 3 km/hr in still water. If the velocity of the stream be 2 km/hr, the time taken by him to swim to a place 10 km upstream and back is ?

1. Speed upstream = (3 - 2) km/hr = 1 km/hr
Speed downstream = (3 + 2) km/hr = 5 km/hr

##### Correct Option: D

Speed upstream = (3 - 2) km/hr = 1 km/hr
Speed downstream = (3 + 2) km/hr = 5 km/hr
Total time taken = (10/1 + 10/5) hr = 12 hrs.

1. A man can row three quarters of a kilometre against the stream in 111/ 4 minutes and return in 71/ 2 minutes. The speed of the man in still water is ?

1. Speed upstream = (3/4) x (4/45 x 60 km/hr = 4 km/hr
Speed upstream = (3/4) x (2/15) x 60 km/hr = 6 km/hr

##### Correct Option: D

Speed upstream = (3/4) x (4/45 x 60 km/hr = 4 km/hr
Speed upstream = (3/4) x (2/15) x 60 km/hr = 6 km/hr
∴ Speed in still water = (4 + 6)/2 km/hr = 5 km/hr

1. A man can row 91/3 in still water and he finds that it takes him thrice as much time to row up than as to row down the same distance in river. The speed of the current is ?

1. Let speed upstream = x km/hr

Then, speed downstream = 3x km/hr
∴ Speed in still water = (x + 3x)/2 km/hr = 2x km/hr

Speed of the current = (3x - x)/2 km/hr = x km/hr

##### Correct Option: D

Let speed upstream = x km/hr

Then, speed downstream = 3x km/hr
∴ Speed in still water = (x + 3x)/2 km/hr = 2x km/hr

Speed of the current = (3x - x)/2 km/hr = x km/hr

&becaus 2x = 28/3
∴ x = 14/3 = 42/3 km/hr.

1. The current of a stream runs at 1 km/hr. A motor boat goes 35 km upstream and back again to the starting point in 12 hours. The speed of motor boat in still water is ?

1. Let the speed in still water be x km/hr
∵ 35/(x - 1) + 35/(x + 1) = 12

##### Correct Option: A

Let the speed in still water be x km/hr
∵ 35/(x - 1) + 35/(x + 1) = 12
⇒ 35(2x) = 12(x2 - 1)
⇒ 12x2 - 70x - 12 = 0
⇒ 12x2 - 72x + 2x - 12 = 0
⇒ 12x(x - 6) + 2 (x - 6) = 0
⇒ (x - 6) (12x + 2) = 0
∴ x = 6 km/hr