SOLUTION: 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
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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!!! Found 2 solutions by checkley77, CharlesG2:Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! x=y+1
xy/(x+y)=1.2
Substitute (y+1) for x & solve for y
(y+1)y/(y+1+y)=1.2
(y^2+y)/(2y+1)=1.2 cross multiply.
y^2+y=1.2(2y+1)
y^2+y=2.4y+1.2
y^2+y-2.4y-1.2=0
y^2-1.4y-1.2=0
(y-2)(y+.6)=0
y-2=0
y=2 hours for Henry.
x=2+1=3 hours for George.
Proof:
2*3/(2+3)=1.2
6/5=1.2
1.2=1.2
You can put this solution on YOUR website! 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
(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
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