SOLUTION: My father-in-law used to have a garden in our backyard. We worried about him weeding the whole garden by himself so we usually sent one of our children out to help. Now, if my son

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Question 401492: My father-in-law used to have a garden in our backyard. We worried about him weeding the whole garden by himself so we usually sent one of our children out to help. Now, if my son worked on the garden by himself it would take him 4 hours longer to weed the garden than his grandfather took. However, if he worked with my father-in-law, he worked twice as fast. Develop a formula for how long it took for both of them to weed the whole garden working together. Simplify/reduce to lowest terms.
How long it took my father-in-law and my son to weed the garden together. If it took an hour and a quarter for them to weed the garden together, how long did it take my son working by himself?


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
if my son worked on the garden by himself it would take him 4 hours longer to
weed the garden than his grandfather took.
However, if he worked with my father-in-law, he worked twice as fast.
Develop a formula for how long it took for both of them to weed the whole garden working together.
Simplify/reduce to lowest terms.
:
let s = time required by son by himself
then
(s-4) = time required by grandpa by himself
and
.5s = son if he works with grandpa (he works twice as fast, it says)
:
Let the completed job = 1; (a weed-free garden)
:
Let t = time when they work together
:
t%2F%28.5s%29 + t%2F%28%28s-4%29%29 = 1
multiply by .5s(s-4)
t(s-4) + .5s(t) = .5s(s-4)
st - 4t + .5st = .5s^2 - 2s
1.5st - 4t = .5s^2 - 2s
Factor out t
t(1.5s - 4) = .5s^2 - 2s
t = %28%28.5s%5E2-2s%29%29%2F%28%281.5s-4%29%29
where
t = time working together
s = son working alone
:
:
If it took an hour and a quarter for them to weed the garden together, how long did it take my son working by himself?
:
%28%28.5s%5E2-2s%29%29%2F%28%281.5s-4%29%29 = 1.25
.5s%5E2-2s = 1.25(1.5s-4)
.5s^2 - 2s = 1.875s - 5
.5s^2 - 2s - 1.875s + 5 = 0
.5s^2 - 3.875s + 5 = 0
s^2 - 7.75s + 10 = 0
Solve this using the quadratic formula
the reasonable solution: s = 6.11 hrs, the son working alone