A motorboat takes 6 hour to cover 100km upstream and 30 km downstream.if the motorboat goes 75km downstream and returns back to its starting point in 8 hours.find the speed of the boet in still water and the 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
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.