Question

Ariv can row his boat 36 km downstream and 32 km in 7 hours. moreover he can row his boat 48 km downstream and 40 km upstream in 9 hours. find the speed of ariv's boat in still water and in flow of the stream.

Answer 1

Answer:

x=10km/ph y=2km/ph

Step-by-step explanation:

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

Distancw = 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

Answer 2

Answer:

Let the speed of the boat in still water be x km/hr and the speed of the stream but y km/hr. Then,

Speed upstream =(x−y)km/hr

Speed downstream =(x+y) km/hr

Now, Time taken to cover 32km upstream =x−y32 hrs

Time taken to cover 36 km downstream =x+y36 hrs

But, total time of journey is 7 hours.

∴x−y32+x+y36=7 ..(i)

Time taken to cover 40km upstream =x−y40

Time taken to cover 48 km downstream =x+y48

In this case, total time of journey is given to be 9 hours.

∴x−y40+x+y48=9 (ii)

Putting x−y1=u and x+y1=v in equations (i) and (ii), we get

32u+36v=7⇒32u−36v−7=0 ..(iii)

40u+48v=9⇒40u−48v−9=0 ..(iv)

Solving these equations by cross-multiplication, we get

36×−9−48×−7u