Question

A boat takes 9 hrs to travel from A to B upstream.If the river current is 3kmph.How long will it take to travel down stream between B & A?

Answer 1

Answer :
         Let Velocity  of boat =  x km/hr
         River Current = 3km/hr
         Net upstream speed=  (x - 3 ) km/hr
         Net Downstream speed  = (x+3 ) km/hr
         Upstream time = 9 hrs
         Let distance between A and B = d km

we know that ,
       speed = distance / time
       Upstream :
             x - 3  =  d / 9
          or 9(x -3) = d ...................... 1st
for Understanding Purpose Only: 
         (
            9 = d/x-3
           by Hit and Trial , we can have
                         d= 27 km and x=6km/hr )
DownStream  :
           Let the boat takes time = T to travel between A and B .
         x+3 = d / T
         T(x+3) = d  -------------- 2nd
from 1st and 2nd , we get
           T(x+3) = 9 (x-3)
           or T = 9(x-3)/x+3
for Understanding Purpose Only:              
 (if U use Hit and Trial of Equation 1st you can have T = 3 hours)
Here we can have T in terms of x , because distance between A and B is not given .

So we can have value of T in terms of x or d only.

Hope this helps you!!

Thank You!!