Question 84642
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