Question 255743
It takes George 1 hour longer to mow the lawn than it takes Henry. Working together, using two mowers, they can mow the lawn in 1 hour and 12 minutes. How long would it take Henry to mow the lawn by himself? 

Thank you!!!

G=time George in hours for one lawn, H=time Henry in hours for one lawn

after 1.2 hours George 1.2/G 
                Henry  1.2/H

1.2/G + 1.2/H = 1
G=1+H

1.2+(1.2G)/H = G
1.2H+1.2G=GH
1.2H+1.2(1+H)=(1+H)H
1.2H+1.2+1.2H=H+H^2
2.4H+1.2=H+H^2
1.4H+1.2=H^2
-H^2+1.4H+1.2=0
H^2-1.4H-1.2=0

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-(-1.4) +- sqrt( (-1.4)^2-4*(1)*(-1.2) ))/(2*1) }}}
{{{x = (1.4 +- sqrt( 1.96-4*(-1.2) ))/2 }}}
{{{x = (1.4 +- sqrt( 1.96+4.8 ))/2 }}}
{{{x = (1.4 +- sqrt( 1.96+4.8 ))/2 }}}
{{{x = (1.4 +- sqrt( 1.96+4.8 ))/2 }}}
{{{x = (1.4 +- sqrt( 6.76 ))/2 }}}
{{{x = (1.4 +- sqrt( 6.76 ))/2 }}}
{{{x = (1.4 +- 2.6)/2 }}}
{{{x = (1.4 + 2.6)/2 }}}
{{{x = 4/2 }}}
{{{x = 2 }}}
{{{x = (1.4 - 2.6)/2 }}}
{{{x = -1.2/2 }}}
{{{x = -0.6 }}}
(h-2)(h+0.6)=0

so Henry can do it in 2 hours
and George in 3 hours

1.2/G + 1.2/H = 1
1.2/3 + 1.2/2 = 1
0.4   +   0.6 = 1
1=1