Answer:
Step-by-step explanation:
Given
George take 1 hr longer than Henry
Let Henry take x hr to complete the work
Therefore time taken by George is x+1 hr
Rate of George is [tex]\frac{1}{x+1} \hr[/tex]
Rate of Henry is [tex]\frac{1}{x} \hr[/tex]
They both complete the work in 1 hr and 12 min i.e [tex]\frac{6}{5} hr[/tex]
therefore they both mow in hr
[tex]\frac{1}{x+1}+\frac{1}{x}=\frac{5}{6}[/tex]
[tex]\frac{x+x+1}{(x+1)(x)}=\frac{5}{6}[/tex]
[tex]5x^2-7x-6=0[/tex]
[tex](x-2)(5x+3)=0[/tex]
[tex]x=2 hr[/tex]
thus George mow [tex]\frac{1}{3}[/tex] lawn in 1 hr
Henry mow [tex]\frac{1}{2}[/tex] lawn in 1 hr
both mow [tex]\frac{5}{6}[/tex] in 1 hr
