Question

a motorboat whose speed is 18 kilometre per hour in still water takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of the stream

Answer 1

$\textsf{Answer :}$

Speed of the stream will be 6 km/hr.

$\textsf{Step-by-step explanation :}$

Given,

Speed of motorboat in still water = 18 km/hr

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

Now, speed of the boat upstream = speed of boat in still water - speed of the stream

⇒ Speed of the boat upstream = $(18-x)$ km/hr

Also, speed of the boat downstream = speed of boat in still water + speed of the stream

⇒ Speed of the boat downstream = $(18+x)$ km/hr

Now, according to question -

Time of upstream journey = Time of downstream journey + 1 hr

$\implies \frac{24\:km}{18-x\:km/hr}=\frac{24\:km}{18+x\:km/hr}+1\:hr$

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

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

$\implies 48x=324-x^{2}$

$\implies x^{2}+48x-324=0$

$\implies x^{2}+54x-6x-324=0$

$\implies x(x+54)-6(x+54)=0$

$\implies (x+54)(x-6)=0$

$\implies x+54=0\:or\:x-6=0$

$\implies x=-54\:or\:x=6$

Since, speed can't be negative therefore -54 is neglected.

Thus, the speed of the stream is 6 km/hr.

Answer 2

Answer:

Let the speed of stream be x km / hr

For upstream = ( 18 - x ) km / hr

For downstream = ( 18 + x ) km / hr

A.T.Q.

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

48 x = 324 - x²

x² + 48 x - 324 = 0

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

x = - 54 or x = 6

Since speed can't be negative .

Therefore , speed of the stream is 6 km / hr .