Question

A motor boat whose speed is 18km/hr in still water takes 1hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

Hey Mate❤❤
here's ua answer :
given that speed of the boat=18km/hr
let the speed of the stream=x km/hr

For upstream
speed=(18-x)
distance=24 km
speed=distance/time upstream
(18-x)=24/time upstream
time upstream=24/(18-x)

For downstream
speed=( 18+x)
distance=24 km
speed=distance / time downstream
(18+x)=24/time downstream
time downstream=24/ ( 18+x)

Given that
time taken upstream is 1 hr more than time taken downstream
time upstream=time downstream+1
24/(18-x)=24/(18+x)+1
24/(18-x)-24/(18+x)=1
24((18+x)-(18-x)/(18-x)(18+x)=1
24(18+x-18+x)/(18-)(18+x)=1
24 ( 2x ) / ( 18-x ) ( 18 + x ) = 1
48x / ( 18-x ) ( 18 + x ) = 1
48x= (18-x)(18+x)
48x=(18 raise to power 2)-(x raise to power2)
48x=324-(x raise to power2)
x raise to power2 +48x-324=0
comparing equations=(a)(x raise to power2)+bx+c=0
D=(b raise to power2)-4ac
D=(48 raise to power2)-4×1×(-324)
D=2304+4×324
D=2304+1229
D=3600

Since x is the speed so It can't be negative
so x=6 is the solution of the equation.
Therefore speed of stream (x)=6km/hr.....
HOPE IT HELPS UH
bye see uh again

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 .