Question 40857
let speed of boat in still water be x mph


speed upstream = x-2
speed downstream = x+2


speed = distance/time


So, x-2 = 5/t
and x+2 = 7/t


The time in both journeys is the same, so i have them both as "t". We get:


t = 5/(x-2) = 7/(x+2)
{{{ 5/(x-2) = 7/(x+2) }}}
{{{ 5(x+2) = 7(x-2) }}}
{{{ 5x+10 = 7x-14 }}}
{{{ 10 = 2x-14 }}}
{{{ 24 = 2x }}}
--> x = 24/2
so x = 12 mph


Check:
upstream: speed is 10mph. 5 miles takes 2 hours
downstream: speed is 14mph. 7 miles takes 2 hours too.


jon