SOLUTION: 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

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. Thank you so much.
Found 2 solutions by rwm, lwsshak3:
Answer by rwm(914) (Show Source): You can put this solution on YOUR website!
Bill can do it in x hours alone
Joe can do it in x+2 hours
Bill does 1/x of the job every hour and 10/x in 10 hrs
Joe does 1/(x+2) of the job in one hour and 10/(x+2) in 10 hrs.
together they do one job in 10 hrs.
This tells that each of them takes more than 10 hrs alone.
10/x+10/(x+2)=1
about 19 hrs for Bill and about 21 hrs for Joe.
10/19 +10/21=1

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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.
..
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:

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
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