Question 311925
Let {{{x}}} = time it takes one pipe to fill tank in hrs
Then {{{x + 15}}} = hrs other pipe takes to fill tank
Add the rates of each pipe to fill tank to get
the rate of both filling tank together
(1 tank/x hrs) + (1 tank/x + 15 hrs) = (1 tank/10 hrs)
{{{1/x + 1/(x + 15) = 1/10}}}
Multiply both sides by {{{x*(x + 15)*10}}}
{{{10*(x + 15) + 10x = x*(x + 15)}}}
{{{10x + 150 + 10x  = x^2 + 15x}}}
{{{x^2 - 5x - 150 = 0}}}
Use quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = -5}}}
{{{c = -150}}}
{{{x = (-(-5) +- sqrt( (-5)^2-4*1*(-150) ))/(2*1) }}}
{{{x = (5 +- sqrt( 25 + 600 ))/2 }}}
{{{x = (5 + 25)/2}}}
{{{x = 15}}} (there is a (-) answer, but I can't use it
{{{x + 15 = 30}}}
One pipe takes 15 hrs
the other pipe takes 30 hrs
check:
{{{1/15 + 1/30 = 1/10}}}
multiply both sides by {{{30}}}
{{{2 + 1 = 3}}}
OK