Question

A boat covers 32km upstream and 36km downstairs in 7hrs. Also it covers 40km upstream and 48km down stream in 9hrs. Find the speed of the boat in still water and that of the stream.

Answer 1

EQ are
VW+VB=32/7. 1
vb-vw=36/7. 2
VW+VB=40/9. 3
vb-vw=48/9. 4
after solving 3 and 4
VB=4.8km/h
vw=0.3km/h

Answer 2

Hey

Here is your answer,

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 = 2 kmph

Hope it helps you!