A motorboat covers a distance of 16 km upstream

Asked by admin @ 13/08/2021 in Math viewed by 274 People

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.5

Answered by admin @ 13/08/2021

Answer:

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= 1
/12

Putting the value of u in (4), we get, v= 1
/4

⇒x+y=12 and x−y=4

2x = 16 =>x = 8

and 8 + y = 12 => y = 4

Thus, speed of the boat in still water =8 km/hr

Speed of the boat in stream = 4 km/hr

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