Question

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

Answer 1

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

Speed of the boat upstream = Speed of boat in still water – Speed of the stream

∴ Speed of the boat upstream = ( 18 – x ) km/hr

Speed of the boat downstream = Speed of boat in still water + Speed of the stream

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

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

Time taken going upstream, 

tup=Distance upstream
Speed upstream =2418−xtup=Distance upstream
Speed upstream =2418−x

tup=2418−xtup=2418−x  -------- (1)

Time taken going downstream,

 tdown=Distance downstream
Speed downstream =2418+xtdown=Distance downstream
Speed downstream =2418+x

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

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

2418−x=2418+x+12418−x=2418+x+1

24(18+x)=24(18−x)+(18+x)(18−x)24(18+x)=24(18−x)+(18+x)(18−x)

24∗18+24x=24∗18−24x+182−x224∗18+24x=24∗18−24x+182−x2

x2+48x−182=0x2+48x−182=0

x2+54x−6x−324=0x2+54x−6x−324=0

(x+54)(x−6)=0(x+54)(x−6)=0

x =6  (Rejecting negative value of x)

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

hope it helps

Answer 2

Let the speed of the stream be x km/hr therefore, the speed of the boat upstream (18-x) km/hr and speed of the boat down stream (18+x)
The time taken to go upstream =distance/speed =24/18-x
~Time taken to go downstream =24/18+x
Acc to question
24/18-x - 24/18+x=1
24(18+x) - 24(18-x) =(18-x) (18+x)
X2 +48x-324=0
Using quadratic formula
X=-48±√48square+1296=-48±√3600/2
=-48±60/2=6or-54
Since x is the speed of the stream, it cannot be negative. So, we ignore the root x=-54therefore, x=6gives
The speed of the stream as 6km/hr
Downstream=18+x=18+6=24
Upstream=18-x=18-6=12