SOLUTION: I am having difficulty understanding how to set up and solve this word problem. My professor says this can be done with a form of quadratic equation. Please help! "It takes Bill

Question 84642This question is from textbook Intermediate Algebra
: I am having difficulty understanding how to set up and solve this word problem. My professor says this can be done with a form of quadratic equation. Please help!
"It takes Billy 2 hours longer to do a certain job than it takes Reena. They worked together for 2 hours; then Reena left and Billy finished the job in 1 hour. How long would it take each of them to do the job alone?"
Thank you for your help,
para.lax This question is from textbook Intermediate Algebra

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x equal the time it takes Reena, so x+2 is the time it takes Billy

if a person takes 3 hours to do a job, in 1 hour they will do 1/3 of the job ... this is the KEY principle

Reena works for 2 hours and does 2/x of the job ... Billy works for 3 hours and does 3/(x+2) of the job

together, they do the WHOLE job ... (2/x)+(3/(x+2))=1 ... multiplying by x(x+2) gives 2(x+2)+3x=x(x+2)

2x+4+3x=x^2+2x ... (here's your quadratic) x^2-3x-4=0 ... (x-4)(x+1)=0 ... so x=4 and x=-1 (negative value not realistic)

Reena takes 4 hours to do the job and Billy takes 6 hours
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