Question

Plz answer this ☺

Q _ 35

Don"t give silly answers........↑↑↑

Answer 1

Our target is to find the speed of the stream.

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

Given that speed of the boat in still water = 18km/hr.

We know that Effective speed of the boat upstream =  (18 - x)  --------- (1).

We know that Effective speed of the boat downstream = (18 + x)  -------- (2)


Now, Here comes the interesting part:

Given that the distances between the places = 24km.  --------- (3)

Given that time is taken by the upstream is 1 hour more than the time is taken by the downstream.  ------- (4)

On solving (1),(2),(3),(4), we get

$\frac{24}{18-x} = \frac{24}{18+x} + 1$

$\frac{24}{18-x} - \frac{24}{18+x} = 1$

On cross-multiplication, we get

$\frac{24(18 + x) - 24(18 - x)}{(18 - x)(18 + x)} = 1$

$\frac{432 + 24x - 432 + 24x}{(18 - x)(18 + x)} = 1$

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

48x = 18^2 - x^2

48x = 324 - x^2

x^2 + 48x - 324 = 0

x^2 - 6x + 54x - 324 = 0

x(x - 6) + 54(x + 6) = 0

(x + 54)(x - 6) = 0

x = 6 (or) x = -54.

The speed of the stream cannot be negative.So, x = 6.


Therefore the speed of the stream = 6km/hr.


Hope this helps!  ------------------ Gud Luck

Answer 2

ANSWER
..............


Let the speed of the stream be y km/hr.


= > speed of the boat in still water = 18km/hr.



----------------

Effective speed of the boat upstream = (18 - y)




************Effective speed of the boat downstream = (18 + y) -------- (2)

*********************

××××××××××××××××××××××


the distances between the places = 24km.

_________________

######. time is taken by the upstream is 1 hour

*******. more than the time is taken by the downstream. ----


*********** we get. ****************

{24}{18-y}
_________. =========
{24}{18+y} + 1



******************************


{24}{18-y} -
_______. =. 1
{24}{18+y }



#################

*************we get ***********

** {24(18 + y) - 24.
** (18 - y)}{(18 - y ) (18 + y)} = 1



•••••••••••••••••••••••




====== {432 + 24y. - 432 + 24y }
. {(18 - y )(18 + y )} = 1


====================


Therefore


===================

24y + 24y = (18-y )(18+y )

48y = 18^2 - y ^ 2

48y = 324 - y ^2

= > Y^2 + 48y - 324 = 0

====Y^2 - 6y + 54y - 324 = 0

= Y(y- 6) + 54(y + 6) = 0

= (Y + 54)(y - 6) = 0

Y = 6
_______ (or) _____
x = -54.

The speed of the stream cannot be negative.

So, y = 6.


*********Therefore the speed of the stream = 6km/hr. *********


Y = 6