Let the speed of the boat

in still water = x kmph

Speed of the stream = y kmph

i ) relative speed of the boat in downstream= ( x + y ) kmphDistance travelled = d1 = 36Time = t1 hrt1 = d1 / s1t1 = 36/ ( x + y )

ii) relative speed of the boat in upstream = ( x - y ) kmphDistance = d2 = 32 kmTime = t2 t2 = 32/ ( x - y )Therefore ,Total time = 7 hrt1 + t2 = 7hr36 / ( x + y ) + 32/ ( x - y ) = 7 ----( 1 )

iii) second time ,Relativespeed of the boat indownstream = ( x + y ) kmphd3 = 48 kmTime = t3t3 = 48/ ( x + y )

iv ) in upstream

Relative speed of the boat = ( x - y ) kmph

time = t4 hrd4 = 40kmt4 = 40/ ( x - y )

Total time = 9 hr48 / ( x + y ) + 40/ ( x - y ) = 9 ---( 2 )

Let 1 / ( x + y ) = a ,1 / ( x - y ) = b

Then rewrite ( 1 ) and ( 2 ) we get 36 a + 32 b = 7 -----( 3 )48a + 40b = 9 ------( 4 )

Multiply ( 4 ) with 4 and equation ( 3 ) with 5 and

192a + 160b = 36 ---( 5 )

180a + 160b = 35 -----( 6 )

Subtract ( 6 ) from ( 5 )

we get

a = 1/ 12

put a = 1/ 12 in ( 3 )we get ,b = 1/ 8Now 1/ ( x + y ) = 1/ 12 1/ ( x - y ) = 1/ 8

Therefore ,

x + y = 12 ----( 7 )x - y = 8 ----- ( 8 )add ( 7 ) and ( 8 )2x = 20x = 10put x = 10 in ( 7 ) we get y = 2

Speed of the boat in still water = x = 10 kmphspeed of the stream= y = 2kmph