Boats and Streams Examples

In this class, We discuss Boats and Streams Examples.

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Example 1:

A man can row upstream at 7kmph and downstream at 10kmph.

Find man’s rate in still water and rate of current?

Solution:

Given, upstream = b = 7

downstream = a = 10

Speed of man in still water = x = 1/2(a+b)

Formulae discussed in the previous class.

x = 1/2(10+7) = 8.5 kmph

Speed of the stream = y = 1/2(a-b)

y = 1/2(10-7) = 1.5 kmph.

Example 2:

A man takes 3 hours 45 minutes to row a boat 15 km downstream a river.

The same man takes 2 hours 30 minutes to cover a distance of 5 km upstream.

Find the speed of the river current in kmph?

Solution:

From the formulae, we can identify the speed of the stream if upstream and downstream are provided.

The question provides distance and time to identify upstream and downstream.

Speed = Distance / Time

Downstream = 15/3 3/4 = 15 * 4/15 = 4 kmph

Upstream = 5/ 2 1/2 = 5 * 2/5 = 2 kmph.

Speed of the current = 1/2(a-b) where a is downstream and b is upstream.

Speed of current = 1/2(4-2) = 1kmph.

Example 3:

A man can row 18 kmph in still water.

It takes him thrice as long to row up as to row down.

Find the rate of the stream?

Solution:

Mans rate upstream = x kmph

mans rate downstream = 3x kmph.

Given the speed of the boat in still water = 18 kmph.

From the formulae speed of the boat in still water given upstream and downstream = 1/2(a+b)

18 = 1/2(3x + x)

x = 9

upstream = x = 9

downstream = 3x = 27

From the formulae, we can find the speed of the stream given upstream and downstream.

speed of the stream = 1/2(a-b)

1/2(27-9)

speed of the stream = nine kmph.