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 329121: 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 x = time required by son working alone
then
(x-4) = time required by grandad alone
:
If son works twice as fast:
.5x = time when son working with grandad
;
Let completed job = 1 (A weeded garden)
:
Let t = time to complete the job working together
:
t%2F%28%28x-4%29%29 + t%2F%28.5x%29 = 1
:
Multiply by .5x(x-4), results
.5xt + t(x-4) = .5x(x-4)
:
.5xt + xt - 4t = .5x^2 - 2x
:
1.5xt - 4t = .5x^2 - 2x
Factor out t
t(1.5x - 4) = .5x^2 - 2x
:
Divide both sides by (1.5x-4)
t = %28%28.5x%5E2-2x%29%29%2F%28%281.5x-4%29%29, is the formula
where:
t = time working together
x = son's time working alone