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

Question 150456: 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. The formula
t(t+4)/3t+4 represents how long it took for both of them to weed the whole garden working together.
Using the formula t(t+4)/3t+4, How long would it take the son alone,if it took an hour and a quarter for them to weed the garden together?
Please help?

Answer by stanbon(75887) (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. The formula
t(t+4)/3t+4 represents how long it took for both of them to weed the whole garden working together.
Using the formula t(t+4)/3t+4, How long would it take the son alone,if it took an hour and a quarter for them to weed the garden together?
=====================
Find "t":
[t(t+4)/(3t+4)] = 5/4 hr
[t^2+4t]/[3t+4] = 5/4
Cross-multiply to get:
4t^2+16t = 15t+20
4t^2 + 11t - 20 = 0
4t^2 + 16t-5t -20 = 0
4t(t+4) + 5(t+4) = 0
(t+4)(4t+5) = 0
t = -4 or t = -5/4
--------------------
Comment: These answers are unrealistic.
Is the formula correct? Shoud it be [t(t+4)/3t] + 4 ?
or something else?
Cheers,
Stan H.
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