Question

a motorboat whose speed is 18 km 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

Answer:

speed of stream=6km/h

Step-by-step explanation:

u.s=b-s, u.s=18-s

d.s=b+s, d.s=18+s

distance=24km

time taken u.s=24/(18-s)

time taken d.s=24/(18+s)

then. 24/(18-s)=24/(18+s)+1

24/(18-s)=(24+18+s)/18+s

24(18+s)=(42+s)(18-s)

432+24s=756-42s+18s-s square

s square+42s-18s+24s+432-756=0

s square+48s-324=0

s square+54s-6s-324=0

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

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

s=6,-54

-54 can be neglected as it is - ve.

so speed of stream = 6km/h

Answer 2

Speed of the motorboat = 18km/hr

Speed of the stream = x km/hr

Difference in time = 1 hr

Upstream = 18 - x km/hr

Downstream = 18 + x km/hr

Distance travelled = 24km

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

24x + 432 - 432 + 24x = 1 (18-x)(18+x)

48x = 324 + 18x - 18x - x^2

x^2 + 48x - 324 = 0

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

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

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

x = -54 , 6

Since the distance cannot be in negative, 6km/hr is the speed of the stream.

Upstream = 12km/hr

Downstream, = 24km/hr

Time taken to travel upstream = 2hr

Time taken to travel downstream = 1hr