Question

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

Answer 1

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

Given: Time taken for going upstream is one hour more than the time taken for going downstream. So, tup=tdown+1 ----------(A)

Distance upstream = Distance downstream = 24 km

Speed of the boat going upstream, vup=18−x

Speed of the boat going downstream, vdown=18+x

Time taken going upstream, tup=Distance upstreamSpeed upstream =2418−x

tup=2418−x -------- (1)

Time taken going downstream, tdown=Distance downstreamSpeed downstream =2418+x

or tdown=2418+x --------- (2)

Using equation (1), (2) and (A):

2418−x=2418+x+1

24(18+x)=24(18−x)+(18+x)(18−x)

24∗18+24x=24∗18−24x+182−x2

x2+48x−182=0

x2+54x−6x−324=0

(x+54)(x−6)=0

x =6 (Rejecting negative value of x)

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 .