Question

6. The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and return
downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream

Answer 1

Let the speed of stream is x km/h
Then, speed of boat upstream = (15 - x) km/h
speed of boat downstream = (15 + x) km/h

we know,
Time = distance/speed
Now, A/c to question,
30/(15- x) + 30/(15 + x) = 4hrs 30 min = (4 + 1/2) hrs
⇒ 30[ 1/(15 - x) + 1/(15 + x) ] = 9/2
⇒30[ (15 + x ) + (15 - x)]/(15 - x)(15+ x) = 9/2
⇒30 × 30/(225 - x²) = 9/2
⇒900/(225 - x²) = 9/2
⇒100/(225 - x²) = 1/2
⇒200 = 225 - x²
⇒x = ±5
But x ≠ -5 because speed can't be negative.
so, speed of stream = 5 km/h

Answer 2

HELLO DEAR,

let the speed of stream is x km/hr.

speed of boat in upstream = (15-x)km/hr.
speed of boat in downstream = (15+x)km/hr.

now,
we know that, distance = speed*time.
total time = 4hr30min = (4 + 1/2)hr = 9/2hr.

30/(15 - x) + 30/(15 + x) = 9/2

30[1/(15 - x) + 1/(15 + x)] = 9/2

(15 + x + 15 - x)/(225 - x²) = 3/20

(30)*20 = (225 - x²)*3

600/3 = 225 - x²

x² = 225 - 200

x² = 25

x = $\mathbf{(+_-5)km/hr}$

x = 5km/hr , x = -5km/hr$\mathbf{[NEGLECT]}$

hence, the speed of stream = 5km/hr.

I HOPE ITS HELP YOU DEAR,
THANKS