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:

Your answer is given below:-

Step-by-step explanation:

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

Answer 2

Step-by-step explanation:

Please find the attachment.