Question

The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream

Answer 1

Speed of a boat in still water = 11 km/hr
Let the speed of stream = x km/hr.
Distance covered = 12 km.
Time taken = 2 hours 45 minutes

= `2(3)/(4) = (11)/(4)`hours
Now according to the condition

`(12)/(11 - x) + (12)/(11 + x) = (11)/(4)`

⇒ `(12(11 + x + 11 - x))/((11 - x)(11 + x)) = (11)/(4)`

⇒ `(12 xx 22)/(121 - x^2) = (11)/(4)`

⇒ 1331 – 11x² = 4 x 12 x 22 = 1056
⇒ 1331 – 11x² = 1056
⇒ 1331 – 1056 – 11x² = 0
⇒ -11x² + 275 = 0
⇒ x² – 25 = 0  ...(Dividing by -11)
⇒ (x + 5)(x – 5) = 0
Either x + 5 = 0,
then x = –5,
but it is not possible as it is in negative.
or
x – 5 = 0,
then x = 5
Hence speed of stream = 5km/hr.