A motor boat whose speed in still water is 18 km /hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

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Solution

Let the speed of the stream be x km/hr
Speed of the boat in still water = 18 km/hr
Speed of the boat in upstream = (18 - x) km/hr
Speed of the boat in downstream = (18 + x) km/hr

Distance between the places is 24 km.
Time to travel in upstream = $fraction numerator d over denominator 18 minus x end fraction$ hr
Time to travel in downstream = $fraction numerator d over denominator 18 plus x end fraction$ hr
Difference between timings = 1 hr

$\frac{24}{18 - x} - \frac{24}{18 + x} = 1 \frac{1}{18 - x} - \frac{1}{18 + x} = \frac{1}{24} \frac{2 x}{324 - x^{2}} = \frac{1}{24} \Rightarrow 48 x = 324 - x^{2} \Rightarrow x^{2} + 48 x - 324 = 0$
⇒ (x + 54)(x - 6) = 0
x = - 54 or 6

Speed of the stream cannot be negative.

Therefore, the speed of the stream is 6 km/hr.

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