Sums on Boats and Streams

Introduction

In Nithra Jobs we have given both the questions and answers with formulas for your clear understanding. So start learning boats and streams formulas to gain basic knowledge in this topic.

Formulas to use:

1. Downstream/Upstream:

In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.

2. If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:

Speed downstream = (u + v) km/hr.

Speed upstream = (u - v) km/hr.

3. If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

Speed in still water = (1/2) (a + b) km/hr.

Rate of stream = (1/2) (a - b) km/hr.

1. A man can row downstream at the rate of 24 Kmph and upstream at 7 Kmph. Find the man's rate in still water and rate of current?

Answer: 15.5 Kmph, 8.5 kmph

Explanation:

Rate of still water = 1/2 (Down stream + Upstream)

Down stream = 24 Kmph

Upstream = 7 Kmph

Rate of still water = ( 1 / 2 ) ( 24 + 7 )

= ( 1 / 2 ) * 31

= 15.5 Kmph

Rate of current = 1/2 (Down stream - Upstream)

= ( 1 / 2 ) ( 24 - 7 )

= ( 1 / 2 ) * 17

= 8.5 kmph

Rate in still water and Rate of current = 15.5 Kmph, 8.5 kmph.

2. A man can row 24 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream?

Answer: 12 kmph.

Explanation:

Let man's rate upstream be x kmph Then his rate of downstream = 3x kmph Rate still water = (1 / 2 ) * ( 3x + x ) = 2x 2x = 24

x = 12

Rate of upstream = 12

Rate of downstream = 12 * 3 = 36 (thrice as long to row up) Rate of stream = (1 / 2 ) * ( 36 - 12)

= 12 kmph

Rate of the stream is 12 kmph

3. In a stream running at 2 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water?

Answer: 22 kmph.

Explanation:

Let the speed of motor boat in still water be x kmph Then, speed in downstream = (x + 2) km

Speed in upstream = (x - 2) kmph

Time taken to row 10km & back = (55 / 60 ) [ 10 / ( x + 2 ) ] + [ 10 / ( x - 2 ) ] = ( 55 / 60 )

( 10 ( x- 2 ) + 10 ( x + 2 ) ) / ( x² - 4 ) = ( 55 / 60 ) ( 10x - 20 + 10x + 20) / ( x² - 4 )

= ( 55 / 60 ) 20x / ( x² - 4 ) = ( 55 / 60 )

60 * 20x = 55 * ( x² - 4 )

120x = 55x² - 220

55x² - 220 - 120x = 0

11x² - 24x - 44 = 0 (x - 22) (11x + 2) = 0

x = 22 or x = -2/11 Then x = 22 kmph

Speed of motor boat is 22 kmph.

4. A Boat going upstream takes 7 hours 30 minutes to cover a certain distance, while it takes 5 hours to cover the same distance running downstream. Then what is the ratio of the speed of boat to speed of water current?

Answer: 1 : 5

Explanation:

Let the distance be x km Formula, Speed = Distance / Time Upstream Speed = x / [ 7 ( 1 / 2 ) ]

= x / ( 15 / 2 )

= 2x / 15

Downstream Speed = x / 5

Formula, The speed of boat = ( Downstream Speed + Upstream Speed ) / 2

Formula, The speed of the stream = ( Downstream Speed - Upstream Speed ) / 2

The speed of boat = [ ( x / 5 ) - ( 2x / 15 ) ] / 2

= ( x / 15 ) / 2

= x / 30

The speed of the stream = [ ( x / 5 ) + ( 2x / 15 ) ] / 2

= ( x / 3 ) / 2

= x / 6

The ratio of the speed of boat to speed of water current = ( x / 30 ) : ( x / 6 )

= 1 : 5

The ratio of the speed of boat to speed of water current = 1 : 5.

5. A Boat takes 120 min less to travel to 45 Km downstream than to travel the same distance upstream. If the speed of the stream is 3 Km / hr. Then Speed of Boat in still water is?

Answer: 12 km / hr

Explanation:

Let Speed of Boat in still water be x km / hr Formula, Time = Distance / Speed

Time = Upstream time + downstream time

2 = [ 45 / ( x - 3 ) ] - [ 45 / ( x + 3 ) ]

2 = 45 { [ 1 / ( x - 3 ) ] - [ 1 / ( x + 3 ) ] }

2 / 45 = { [ 1 / ( x - 3 ) ] - [ 1 / ( x + 3 ) ] }

2 / 45 = [ ( x + 3 ) - ( x -3 ) ] / [ ( x + 3 )( x - 3 ) ]

2 / 45 = 6 / ( x² - 9 )

2 / ( 45 * 6 ) = 1 / ( x² - 9 )

1 / ( x² - 9 ) = 1 / 135 ( x² - 9 ) = 135

x² = 144

x = 12 km / hr

Then Speed of Boat in still water is 12 km / hr.

Conclusion

Learn and try to solve these problems in a limited time to develop your fluency. To be selected in a company utilize the above given boats and streams problems with solutions that are given in Nithra Jobs.