Question

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Question] A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km downstream in 9 hours. Find the speed of the boat in still water and that of the stream?
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Answer 1

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−y

32

hrs

Time taken to cover 36 km downstream =

x+y

36

hrs

But, total time of journey is 7 hours.

∴

x−y

32

+

x+y

36

=7 ..(i)

Time taken to cover 40km upstream =

x−y

40

Time taken to cover 48 km downstream =

x+y

48

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

∴

x−y

40

+

x+y

48

=9 (ii)

Putting

x−y

1

=u and

x+y

1

=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×−7

u

=

32×−9−40×−7

−v

=

32×48−40×36

1

⇒

−324+336

u

=

−288+280

−v

=

1536−1440

1

⇒

12

u

=

8

v

=

96

1

⇒u=

96

12

and v=

96

8

⇒u=

8

1

and v=

12

1

Now, u=

8

1

⇒

x−y

1

=

8

1

⇒x−y=8 ..(v)

and, v=

12

1

⇒

x+y

1

=

12

1

⇒x+y=12 ..(vi)

Solving equations (v) and (vi), we get x=10 and y=2

Hence, Speed of the boat in still water =10 km/hr

and Speed of the stream =2km/hr.

Answer 2

Hope it's help you dear...