Question

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a boat covers 36km upstream and 42 km downstream in 7hrs. also it covers 46 km upstream and 52 km downstream.find the speed of the boat in still water and that of the stream​

Answer 1

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−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.