Question 142743
Let x= amount of time it takes Electrician working alone
Then x+9=amount of time it takes the apprentice working alone
Electrician works at the rate of 1/x buildings per day
Apprentice works at the rate of 1/(x+9) buildings per day
Electrician and Apprentice works at the rate of (1/x)+1/(x+9) buildings per day and we are told that the Electrician and Apprentice works at the rate of 1/20 building per day, so:

(1/x)+1/(x+9)=1/20 multiply each term by 20x(x+9)
20(x+9)+20x=x(x+9)  get rid of parens

20x+180+20x=x^2+9x  subtract 40x and also 180 from each side

20x+20x-40x+180-180=x^2+9x-40x-180 or

x^2-31x-180=0------------------quadratic in standard form and it can be factored:
(x-36)(x+5)=0

Disregard the negative value for x; time in this case is positive
x-36=0
x=36 days-----------------------------------------time it takes electrician working alone
x+9=36+9=45 days time it takes the apprentice working alone

CK
1/36 + 1/45 = 1/20  multiply each term by 180

5+4=9
9=9

Hope this helps---ptaylor