Question 329121
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/((x-4))}}} + {{{t/(.5x)}}} = 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 = {{{((.5x^2-2x))/((1.5x-4))}}}, is the formula
where:
t = time working together
x = son's time working alone