Problems on Boats and Streams

Introduction

In this article we will see about boats and streams solved questions. This will involve looking at how these concepts apply in different contexts and applying them to solve various problems through Nithra Jobs.

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. The speed of a boat in still water is 30 kmph and the speed of the current is 25 kmph. Find the speed downstream and upstream?

Answer: 55 kmph, 5 kmph

Explanation:

Given data, Speed in still water = 30 kmph and Speed of the stream = 25 kmph

Formula, Downstream Speed = Speed in still water + speed of the stream

Formula, Upstream Speed = Speed in still water - speed of the stream

Downstream Speed = 30 + 25

= 55 kmph

Upstream Speed = 30 - 25

= 5 kmph

∴ Downstream Speed, Upstream Speed = 55 kmph, 5 kmph.

2. A man rows his boat 72 km downstream and 34 km upstream, taking 2 hours each time. Find the speed of the stream?

Answer: 9.5 kmph

Explanation:

For downstream, distance = 72 km and Time = 2 hours

For Upstream, distance = 34 km and Time = 2 hours

Formula, Speed = distance / time Downstream Speed = 72 / 2

= 36 kmph

Upstream Speed = 34 / 2

= 17 kmph

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

= ( 36 - 17 ) / 2

= 19 / 2

= 9.5 kmph

∴ The speed of the stream = 9.5 kmph.

3. A man can row 4 kmph in still water. When the river is running at 1.5 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man?

Answer: 3.4375 km

Explanation:

Let the distance travelled by the man be x

Given data, Total time to row to a place and back = 1 hour,

Speed in still water = 4 kmph and

Speed of the stream = 1.5 kmph

Formula, Downstream Speed = Speed in still water + speed of the stream

Formula, Upstream Speed = Speed in still water - speed of the stream

Downstream Speed = 4 + 1.5

= 5.5 kmph

Upstream Speed = 4 - 1.5

= 2.5 kmph

Total time = Upstream time + downstream time Formula,

Time = Distance / Speed

1 = ( x / 5.5 ) + ( x / 2.5 )

1 = ( 2.5 x + 5.5 x ) / ( 5.5 * 2.5 )

1 = 8x / ( 5.5 * 2.5 )

8x = ( 5.5 * 2.5 )

x = ( 5.5 * 2.5 ) / 8

x = 13.75 / 8

x = 1.71875

The total distance travelled by the man to row to a place and back = x + x = 2x

= 2 * 1.71875

= 3.4375 km

∴ The total distance travelled by the man to row to a place and back = 3.4375 km.

4. The speed of a boat in still water is 20 kmph and the speed of the current is 15 kmph. Find the speed downstream and upstream?

Answer: 35 kmph, 5 kmph

Explanation:

Given data, Speed in still water = 20 kmph and Speed of the stream = 15 kmph

Formula, Downstream Speed = Speed in still water + speed of the stream Formula, Upstream Speed = Speed in still water - speed of the stream Downstream Speed = 20 + 15 = 35 kmph

Upstream Speed = 20 - 15

= 5 kmph

∴ Downstream Speed, Upstream Speed = 35 kmph, 5 kmph.

5. A man rows his boat 62 km downstream and 32 km upstream, taking 2 hours each time. Find the speed of the stream?

Answer: 7.5 kmph

Explanation:

For downstream, distance = 62 km and Time = 2 hours

For Upstream, distance = 32 km and Time = 2 hours

Formula, Speed = distance / time Downstream Speed = 62 / 2

= 31 kmph

Upstream Speed = 32 / 2

= 16 kmph

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

= (31 - 16) / 2

= 15 / 2

= 7.5 kmph

∴ The speed of the stream = 7.5 kmph.

Conclusion

These aptitude set of questions that may be asked in an exam. It will help you to get high scores in boats and stream concepts.