Question

A boat covers 32 km upstream & 36 km downstream in 7 hours. Also it can cover 40 km upstream and 48 km downstream in 9 hours. Find the speed of board in still water and that of the stream
Answer this fast guys

Answer 1

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 ) kmph

Distance travelled = d1 = 36

Time = t1 hr

t1 = d1 / s1

t1 = 36/ ( x + y )

ii) relative speed of the boat in upstream
= ( x - y ) kmph

Distance = d2 = 32 km

Time = t2

t2 = 32/ ( x - y )

Therefore ,

Total time = 7 hr

t1 + t2 = 7hr

36 / ( x + y ) + 32/ ( x - y ) = 7 ----( 1 )

iii) second time ,

Relativespeed of the boat in downstream
= ( x + y ) kmph

d3 = 48 km

Time = t3

t3 = 48/ ( x + y )

iv ) in upstream Relative speed of the boat
= ( x - y ) kmph time = t4 hr

d4 = 40km

t4 = 40/ ( x - y )

Total time = 9 hr

48 / ( 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/ 8

Now,
1/ ( x + y ) = 1/ 12
1/ ( x - y ) = 1/ 8

Therefore ,

x + y = 12 ----( 7 )
x - y = 8 ----- ( 8 )

add ( 7 ) and ( 8 )

2x = 20

x = 10

put x = 10 in ( 7 )

we get,

y = 2

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