a motorboat takes 6 hours to cover 100km downstream and 30km upstream. If the motor boat goes 75km downstream and returns back to the starting point in 8hrs. Find the speed of the motorboat in still water and speed of the 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
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.
Answer:
take x-y p and x+y q
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