Question 327804
John takes 3 hours longer than Andrew to peel 500 pounds (lb) of apples.
 If together they can peel 500 lb of apples in 8 hours, then how long would it
 take each one working alone.
:
Let t = time required by Andrew
then
(t+3) = time required by John
:
Let the completed job = 1; (the peeling of 500 lb of potatoes)
:
Each person will do a fraction of job, the two fractions add up to 1
{{{8/t}}} + {{{8/(t+3)}}} = 1
Multiply by t(t+3),
results:
8(t+3) + 8t = t(t+3)
:
8t + 24 + 8t = t^2 + 3t
:
16t + 24 = t^2 + 3t
Arrange as quadratic equation
t^2 + 3t - 16t - 24 = 0
:
t^2 - 13t - 24 = 0
Use the quadratic formula to find t
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
x=t, a=1, b=-13, c=-24
{{{t = (-(-13) +- sqrt(-13^2-4*1*-24 ))/(2*1) }}}
:
 {{{t = (13 +- sqrt(169-(-96) ))/2 }}} 
:
{{{t = (13 +- sqrt(265 ))/2 }}}
The positive solution is what we want here:
{{{t = (13 + 16.279)/2 }}}
t = {{{29.279/2}}}
t = 14.64 hrs, Andrew working alone
then
14.64+3 = 17.64 hrs, John working alone
:
:
Check solution
{{{8/14.64}}} + {{{8/17.64}}} = 
 .546 + .454 = 1