Question

A motorboat covers a distance of 16km upstream and 24km downstream

in 6 hours. In the same time it covers a distance of 12 km upstream and

36km downstream. Find the speed of the boat in still water and that of the

stream.​

Answer 1

ANSWER

Let speed of the boat in still water =x km/hr, and

Speed of the current =y km/hr

Downstream speed =(x+y) km/hr

Upstream speed =(x−y) km/hr

T=

S

D

x+y

24

+

x−y

16

=6 .......(1)

x+y

36

+

x−y

12

=6 .......(2)

Put

x+y

1

=u and

x−y

1

=v the above equation becomes,

24u+16v=6

Or, 12u+8v=3 ... (3)

36u+12v=6

Or, 6u+2v=1 ... (4)

Multiplying (4) by 4, we get,

24u+8v=4v … (5)

Subtracting (3) by (5), we get,

12u=1

⇒u=

12

1

Putting the value of u in (4), we get, v=

4

1

⇒

x+y

1

=

12

1

and

x−y

1

=

4

1

⇒x+y=12 and x−y=4

Thus, speed of the boat upstream =4 km/hr

Speed of the boat downstream =12 km/hr