Question

A boat goes 32 km upstream and 34 km downstream in 7 hours also it covers 40 km upstream and 48 km downstream in 9hr find speed of both

Answer 1

Answer:

Speed of the boat in still water = x = 209/15 kmph

Speed of the stream = y = 121/15 kmph

Step-by-step explanation:

Hi ,

Let the speed of the boat in still water = x kmph

Let the speed of the stream = y kmph

i ) relative speed of the boat in downstream

Sd= ( x + y ) kmph

Distance covered during downstream d = 34 km

Time taken during downstream = Td hr

Td= d / Sd

Td = 34/ ( x + y )

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

Distance covered during upstream du = 32 km

Time taken during downstream = Tu hr

Tu= 32/ ( x - y )

Given Total time = 7 hr

Td + Tu = 7 hr

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

Also, it is given that boat covers 40 km upstream and 48 km downstream

in 9hr in another journey

downstream , speed of downstrem = ( x + y ) kmph

d = 48 km

Time during downstream = td

td= 48/ ( x + y )

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

time during upstream = tu hr

d = 40km

tu = 40/ ( x - y )

Given Total time = 9 hr

48 / ( x + y ) + 40/ ( x - y ) = 9 ---( 2 )

Let 1 / ( x + y ) = a ,

1 / ( x - y ) = b

rewriting ( 1 ) and ( 2 ) we get

34 a + 32 b = 7 -----( 3 )

48a + 40b = 9 ------( 4 )

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

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

170a + 160b = 35 -----( 6 )

Subtract ( 6 ) from ( 5 )we get

a = 1/ 22

Substituting a = 1/ 22 in ( 3 ),we get ,

b = 15/88

Now 1/ ( x + y ) = 1/ 22  and

1/ ( x - y ) = 15/88

Therefore ,

x + y = 22 ----( 7 ) and

x - y = 88/15 ----- ( 8 )

adding ( 7 ) and ( 8 ), we get

2x = 418/15

x =209/15,

put x = 209 in ( 7 ) we get

y = 121/15

Speed of the boat in still water = x = 209/15 kmph

Speed of the stream = y = 121/15 kmph

Hope, it helps !