Question : A speedboat, whose speed is 20 km/hr in still water, goes 35 km downstream and comes back in a total of 8 hours. What is the speed of the stream?
Option 1: 20 km/hr
Option 2: 10 km/hr
Option 3: 15 km/hr
Option 4: 5 km/hr
Correct Answer: 15 km/hr
Solution : Given, A speedboat, whose speed is 20 km/h in still water, goes 35 km downstream and comes back in a total of 8 hours. We know, Downstream speed = Speed of boat in still water + Speed of stream and, Upstream speed = Speed of boat in still water - Speed of stream Let the speed of the stream be $x$. The total time = 8 hours ⇒ $\frac{35}{20+x}+\frac{35}{20-x}=8$ ⇒ $\frac{35(20-x)+35(20+x)}{(20+x)(20-x)}=8$ ⇒ $700+700=8(400-x^2)$ [As $(x-y)(x+y)=x^2-y^2$] ⇒ $1400=3200-8x^2$ ⇒ $8x^2=1800$ ⇒ $x^2=\frac{1800}{8}$ ⇒ $x^2=225$ ⇒ $x=15$ Hence, the correct answer is 15 km/hr.
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