a motorboat whose speed is 18 kilometre per hour in still water takes 1 hour 30 minutes more to go 36 kilometre upstream then to return downstream to the same spot. Find the speed of the stream
Answers
Answer:
Speed of boat in still water =18 \; km
Let the speed of stream be x km/hr.
\text{Speed of boat upstream}=\text{Speed of boat in still water }- \text{Speed of stream.}
\text{Speed of boat upstream}=(18-x) \; km/hr
\frac{\text{Time of upstream journey}}{\text{Speed of boat upstream}} = \frac{\text{distance covered downstream}}{\text{Speed of the boat downstream}}
\frac{36}{(18-x)} = \frac{36}{(18+x)}+1 \frac{1}{2}
\frac{36}{(18-x)} - \frac{36}{(18+x)} = \frac{3}{2}
\frac{648+36x-648+36x}{(18-x)(18+x)} = \frac{3}{2}
72x =(324-x^2) \left ( \frac{3}{2} \right )
144x =972-3x^2
3x^2+144x-972=0
Divide by 3
x^2+48x-324=0x=6,x\neq -54Th
x^2-6x+54x-324=0
x(x-6)+54(x-6)=0
(x-6)(x+54)=0
The speed of the stream 1 is 6 km/hr.
Step-by-step explanation:
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