solution

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.

pls follow tannuranna 59 in my following and me ✌️