A motor boat has a speed of 18 kmhr in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream in km/hr.
6 km/hr
Let the speed of the stream be 'x' and the time required to travel upstream be 't'.
Time=DistanceSpeed
Speed of boat in upstream
= Speed of boat - Speed of stream
= 18 - x
and, speed of boat in downstream
= speed of boat + speed of stream
= 18 + x
∴ From the given data,
t=24(18+x)---------------(1)
t+1=24(18−x)------------(2)
Subtracting (1) from (2), we get
1=24[118−x−118+x]
⇒1=24[2x(182−x2)]
⇒182−x2=48x
⇒x2+48x−182=0
Now, the equation x2+48x−182=0 can also be written as:
x2+2(24)x+242−242−182=0
⇒(x+24)2−900=0
⇒(x+24)2−302= 0
⇒(x+24)2=302
⇒x+24=±30 (Taking square root on both sides)
⇒ x=−54 or x=6
The speed of the stream cannot be negative.
So, the speed of the stream =6 km/hr