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 400724: 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.


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