My father-in-law used to have a garden in our backyard. We worried about him wee

Question

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 3 hours longer to weed the garden than his grandfather took. However, if he worked with my father-in-law, my son worked twice as fast. If it took an hour and twenty minutes for them to weed the garden together, how long did it take my son working by himself?

I tried to do this on my own byut I cannot do quadradic equations could use some help thanks!!

Explanation / Answer

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-3) = 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 : + = 1 :t/(x-3)+t/.5x=1 Multiply by .5x(x-3), results .5xt + t(x-3) = .5x(x-3) : .5xt + xt - 3t = .5x^2 - 1.5x : 1.5xt - 3t = .5x^2 - 1.5x Factor out t t(1.5x - 3) = .5x^2 - 1.5x : Divide both sides by (1.5x-3) t = , is the formula e (.5x^2-1.5x)/(1.5x-3) where: t = time working together x = son's time working alone

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