a motorboat takes total of an 10 hours to cover 120 km upstream and return if it takes 15 hours to cover 150 km upstream and 200 km downstream . find the speed of the boat in still water and speed of stream
Answers
Let the speed of the motor boat in still water be x km/h.
Let the rate of flow of the stream be y km/h
Speed of boat upstream = (x - y) km/h.
Speed of boat downstream = (x + y)km/h.
we know time = distance/speed.
now , A to Q,
Time for 100 km downstream and 30 km upstream
100/(x + y) + 30/(x - y)
And it takes 6 hrs to cover downstream and upstream. Then
100/(x + y) + 30/(x - y) = 6
Time for 75 km downstream and returning (means 75 km upstream)
= 75/(x + y) + 75/(x - y)
Given that the time taken is 8 hours
75/(x + y) + 75/(x - y) = 8
\bold{PUT} \left[\begin{array}{cc}\frac{1}{x + y} = p\:\: and \:\:\frac{1}{x - y}=q\end{array}\right]
now the equation should be .
100p + 30q = 6
50p + 15q = 3------------( 1 )
75p + 75q = 8----------( 2 )
from--------( 1 ) &---------( 2 )
multiply by ( 3 ) in -----( 1 )
250p + 75q = 15
75p + 75q = 8
(–)______(–)____(–)
-------------------------------
175p = 7
p = 1/25 [ put in -------( 1 ) ]
50(1/25) + 15q = 3
2 + 15q = 3
q = 1/15 = 1/(x - y)
x - y = 15------------( 3 )
p = 1/25 = 1/(x + y)
x + y = 25---------( 4 )
From---------( 3 ) &----------( 4 )
x - y = 15
x + y = 25
---------------
2x = 40
x = 20 [ put in ------( 3 ) ]
x - y = 15
20 - y = 15
y = 20 - 15
y = 5 , x = 20
Hence, the speed of the motor boat in still water is 20 km/h and rate of flow of the stream is 5 km/h.
Step-by-step explanation:
- in continuation to teh attachment
150/x+y+200/x-y=15
let x-y=uand x+y=v
150v+200u =15
30v+40u=3
by solving the pair of equa the just above and one inthe attachment we get
v=1/30
and u=3/40
so x+y=30
and x-y=40/3
on taking lcm we get 3x-3y=40
on solving both these equation we get
y=50/6and x= 130/6
hence speed of boat is 130/6and speed of stream is 50/6
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