A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.
Solution
Let the speed of the stream be x km/hr.
speed of the boat in still water = 18 km/hr.
Total Distance = 24 km.
We know that,
Speed of the boat up stream = speed of the boat in still water − speed of the stream
= (18 − x) km/hr
Speed of the boat down stream = speed of the boat in still water + speed of the stream
= (18 + x) km/hr
Time of up stream journey = t1 = \[\frac{24}{18 - x}\]
Time of down stream journey = t2 = \[\frac{24}{18 + x}\]
According to the question,
t1 − t2 = 1 hr
\[\Rightarrow \frac{24}{18 - x} - \frac{24}{18 + x} = 1\]
\[ \Rightarrow \frac{24(18 + x - 18 + x)}{(18 - x)(18 + x)} = 1\]
\[ \Rightarrow \frac{24(2x)}{(18 )^2 - x^2} = 1\]
\[ \Rightarrow 48x = 324 - x^2 \]
\[ \Rightarrow x^2 + 48x - 324 = 0\]
\[ \Rightarrow x^2 + 54x - 6x - 324 = 0\]
\[ \Rightarrow x(x + 54) - 6(x + 54) = 0\]
\[ \Rightarrow (x - 6)(x + 54) = 0\]
\[ \Rightarrow x - 6 = 0 \text { or } x + 54 = 0\]
\[ \Rightarrow x = 6 \text { or } x = - 54\]
Since, speed cannot be negative.
Thus, speed of the stream is 6 km/hr.
