SOLUTION: Please solve: Two front-end loaders can remove 3/4 of the dirt from an excavation in 1 4/5 days. Working alone, loader A would take 2 days longer than loader B working alone to

Question 108260: Please solve:
Two front-end loaders can remove 3/4 of the dirt from an excavation in 1 4/5 days. Working alone, loader A would take 2 days longer than loader B working alone to remove all the dirt. How long for A to do the job completely by itself?
Thanks.
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
3/4=.75 of all the dirt in 1 4/5 or 1.8 days
the full job of removing all the dirt is:
1.8/.75=2.4 days.
to formula for working together is:
(x+y)/xy
(x+x+2)/x(x+2)=1.8
(2x+2)/(x^2+2x)=1.8 now cross multiply
1.8x^2+3.6x=2x+2
1.8x^2+3.6x-2x-2=0
1.8x^2+1.6x-2=0
using the quadratic equation we get:

x=(-1.6+-sqrt[1.6^2-4*1.8*-2])/2*1.8
x=(-1.6+-sqrt[2.56+14.4])/3.6
x=(-1.6+-sqrt[16.96])/3.6
x=(-1.6+-4.12)/3.6
x=(-1.6+4.12)/3.6
x=2.52/3.6
x=.7 days for the B loader.
.7+2=2.7 days for the A loader.
proof
(.7+2.7)/.7*2.7=1.8
3.4/1.89=1.8
1.8=1.8

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