Question 440460
It takes Joe 2 hours longer than Bill to load a truck. If they load it together, they can do it in 10 hours. How long should it take Bill to do it alone? 
I need to describe the variable, variable phrases, write the equation, and solve.
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let x=hours Bill could load the truck doing it alone
Then, 1/x=Bill's hourly work rate
Joe's hourly work rate=1/x+2
Hourly work rate working together=1/10
The sum of individual work rates=work rate when working together
1/x + 1/x+2 = 1/10
LCD=x(x+2)(10)
multiply each term by LCD to get rid of fractions
10(x+2)+10x=x(x+2)
10x+20+10x=x^2+2x
x^2-18x-20=0
solve by quadratic formula below:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1,  b=-18, c=-20
x=(-(-18)+-sqrt((-18)^2-4*1*-20))/2(1)
  =(18+-sqrt(404))/2
  =(18+-20.1)/2
x=19.05hrs
x=-2.1hrs (reject)
ans:
It would take Bill 19.05 hours to complete loading the truck by himself