Boats and Streams

Algebra Level 3

In a stream running at 2 kmph, a motor boat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.(in kmph)


The answer is 22.

Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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1 solution

t = d V t=\dfrac{d}{V} where: t = t i m e ; d = d i s t a n c e ; V = s p e e d t=time;d=distance;V=speed

33 60 = 6 V − 2 + 6 V + 2 \dfrac{33}{60}=\dfrac{6}{V-2}+\dfrac{6}{V+2}

Multiply both sides by ( V − 2 ) ( V + 2 ) (V-2)(V+2) to remove denominators. We have

0.55 ( V − 2 ) ( V + 2 ) = 6 ( V − 2 ) + 6 ( V + 2 ) 0.55(V-2)(V+2)=6(V-2)+6(V+2)

0.55 ( V 2 − 4 ) = 12 V 0.55(V^2-4)=12V

0.55 V 2 − 12 V − 2.2 = 0 0.55V^2-12V-2.2=0

Using the quadratic formula, the speed of the boat in still water is

V = 22 k p h V=22~kph

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