Question

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

Answer 1

Answer:

let the speed of stream be x km/hr

the speed of boat upstream=(18-x) km/hr

and speed of boat downstream =(18+x) km /hr

time taken to go upstream= distance/time

. =24/18-x hours

time taken to go downstream= ____||____

=24/18+x

A.T.Q

24/18-x - 24/18+x = 1

24(18+x) - 24(18-x) = (18-x) (18+x)

x*+48x-324 = 0

we know that

D= b*- 4ac

= 48*-4x1x-324

= 2304 + 1296

= 3600

now,

x = -b+-√d/2a

x = -48 +- √3600/2x1

x = -48 +- 60/2

taking +ve sign

= -48+60/2

= 6

taking -ve sign

= -48-60/2

= -54(indifine)

since speed of boat cannot be -ve

therfore speed of boat is 6km/hr

hope it heplfull

Answer 2

Given: Speed of Motorboat is 18km/hr.

❏ Let the speed of the stream be x km/hr.

Therefore,

Speed of Motorboat in downstream = (18 + x) km/hr.

And,

Speed of Motorboat in upstream = (18 - x) km/hr.

⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

⠀⠀⠀

$\underline{\boldsymbol{According\: to \:the\: Question :}}$ ⠀

⠀⠀⠀

$:\implies\sf \dfrac{24}{18 - x} - \dfrac{24}{18+x} = 1 \\\\\\:\implies\sf \dfrac{24(18 + x) - 24(18 - x)}{(18 - x) (18 +x)} = 1 \\\\\\:\implies\sf \dfrac{24( \:\cancel{18} + x - \:\cancel{18} + x}{(18 - x) (18 +x)} = 1 \\\\\\:\implies\sf \dfrac{24(2x)}{324 - x^2} = 1\\\\\\:\implies\sf 324 - x^2 = 48x\\\\\\:\implies\sf -x^2 - 48x + 324 = 0\\\\\\:\implies\sf x^2 + 48x - 324 = 0\\\\\\:\implies\sf x^2 - 6x + 54x - 324 = 0\\\\\\:\implies\sf x(x - 6) +54(x - 6) = 0\\\\\\:\implies\sf (x -6) (x + 54) = 0\\\\\\:\implies{\underline{\boxed{\frak{\purple{ x = 6 \: and \: -54}}}}}\:\bigstar$

⠀⠀⠀

Ignoring negative value, because speed can't be negative.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\therefore\:{\underline{\sf{Hence, \: speed \: of \ the \: stream \: is\: \bf{6 km/hr}.}}}$