Question 201087
Let {{{c}}} = speed of current
Let {{{b}}} = speed of boat in still water
Let {{{t}}} = time for both trips in hrs
given:
{{{b = 15}}} mi/hr
{{{12 = (15 + c)*t}}}
{{{9 = (15 - c)*t}}}
-------------------
{{{12 = 15t + ct}}}
{{{9 = 15t - ct}}}
Add the equations
{{{21 = 30t}}}
{{{t = 7/10}}} hrs
And, since
{{{12 = (15 + c)*t}}}
{{{12 = (15 + c)*(7/10)}}}
{{{120 = 105 + 7c}}}
{{{7c = 15}}}
{{{c = 2.143}}} mi/hr answer
check:
{{{12 = 15t + ct}}}
{{{12 = 15*.7 + 2.143*.7}}}
{{{12 = 10.5 + 1.5}}}
{{{12 = 12}}}
and
{{{9 = (15 - c)*t}}}
{{{9 = (15 - 2.143)*.7}}}
{{{9 = 12.857*.7}}}
{{{9 = 8.9999}}} close enough