Question

A boat goes 16 km upstream and 24km downstream in 6 hours. Also, it covers 12 km upstream and 36 km downstream in the same time . Find the speed of the boat in still water and that of stream.

Answer 1

s= speed of boat in still water
c= speed of stream
effective speed upstream = (s-c)
effective speed downstream= (s+c)

(16/(s-c))+(24/(s+c))= 6
8/(s-c) + 12/(s+c)= 3. (dividing by 2)--->(i)

12/(s-c) + 36/(s+c) = 6
4/(s-c)+ 12/(s+c)= 2. (dividing by 2)---->(ii)

(i)-(ii)

$\frac{8}{s - c} + \frac{12}{s + c } = 3 \\ \frac{4}{s - c} + \frac{12}{s + c} = 2$
4/(s-c)= 1
4=s-c
s= c+4

using s=c+4 in (i)

(16/(c+4)-c) + 24/(c+4)+c= 6
16/4 + 24/2c+4=6
4 + 24/2c+4=6
24/2c+4= 6-4
24/2c+4= 2
24=4c+8
4c= 16
c=4

s=c+4
s= 4+4
s=8

hope it helps u....
if yes, mark brainliest...
have a great day ahead...

@TeraBhalaHo

Answer 2

Hii friend,

Let the speed of the boat in still water be X km/hr and the speed of the stream be Y km/hr.

Therefore,

Speed upstream = (X-Y) km/hr

And,

Speed downstream= (X+Y) km/hr.

Time taken to cover 16 km upstream =16/(X-Y) hrs.

Time Taken to cover 24 km downstream = 24/(X+Y) hrs

Total Time Taken to cover to both distance=6 hours.

Therefore,

16/X-Y + 24/X+Y = 6.…...(1)

Again,

Time Taken to cover 12 km upstream= 12/(X-Y) hrs

Time Taken to cover 36 km downstream = 36/(X+Y) hrs.

Total Time Taken to cover both Distance =6 hours.

Therefore,

12/X-Y + 36/X+Y = 6.........(2)

Putting 1/(X-Y) = U and 1/(X+Y) = V in equation (1) and (2). we get,

16U + 24V = 6 => 8U + 12V = 3......(3)

12U +36V = 6 => 2U + 6V = 1.......(4)

On multiplying (4) by 4 and subtracting (3) from it , we get,

12V =1

V = 1/12

Therefore,

1/X+Y = 1/12

X+Y = 12.......(5)

On multiplying (4) by 2 subtracting it from (3) we get,

4U = 1

U = 1/4

Therefore,

1/X-Y = U

1/X-Y = 1/4

X-Y = 4.....(6)

On adding (5) and (6) , we get,

2X= 16

X = 16/2 = 8

On subtracting (4) from (5) , we get,

2Y = 8

Y = 8/2 =4


Hence,

Speed of the boat in still water = 8 Km/ hr

And,

Speed of the stream = 4 km/hr.

HOPE IT WILL HELP YOU.... :-)