Question

A boat goes 16 km upstream and 24 km 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 the stream.

Answer 1

Answer:

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)

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

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