Class 10 Math All topics Quadratic Equations

Pratik takes $8$ hours to travel $36$ km downstream and return to the same spot the speed of boat in still water is $12$ kilometre per hour find the speed of water current

Solution:

Let the speed of the current be $x$ km/hr.

Pratik goes $36$ km downstream.

$∴$ Distance covered by the Pratik in Downstream $=36$ km.

Speed of the Pratik in downstream $=(12+x)$ km/hr.

$∴$ Time taken $=(12+x)36 $

Now, He also returned to the same spot.

$∴$ Distance covered in upstream $=36$ km.

Speed of the Pratik in upstream $=(12−x)$ km/hr.

$∴$ Time taken $=(12−x)36 $

Now,

Time taken in upstream $+$ Time taken in downstream $=8$ hrs.

$∴(12−x)36 +(12+x)36 =8$

$⇒36(12+x)+36(12−x)=8(12+x)(12−x)$

$⇒36(12+x+12−x)=8(144−12x+12x−x_{2})$

$⇒36×24=8(144−x_{2})$

$⇒36×3=144−x_{2}$

$∴x_{2}=144−108$

$∴x=36 $

$⇒x=+6$ or $−6$

$−6$ cannot be possible.

$∴$ Speed of the current is $6$ km/hr.

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introduction to trigonometry

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