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.