applications w/ rational expressions

[JayJay06]

Juan can paint a 3600-square-foot house in 12 days, and Carissa can do the same job in only 8 days. How long will take them to paint a 3600-square-foot house if they work together?

Juan

x * 12 = 3600
x = 300

Carissa
a* 8 = 3600
a= 450

together

300 + 450 = 750

I don't know what next step to take. May some one plz help me. Thank you.

 

[Mrspi]

Juan can paint a 3600-square-foot house in 12 days, and Carissa can do the same job in only 8 days. How long will take them to paint a 3600-square-foot house if they work together?

Juan

x * 12 = 3600
x = 300

Carissa
a* 8 = 3600
a= 450

together

300 + 450 = 750

I don't know what next step to take. May some one plz help me. Thank you.

Let x = number of days it takes them to do the job together

Juan can paint the house in 12 days, so each day he does 1/12 of the job. If Juan works for x days, he will paint x/12 of the house

Carissa can paint the house in 8 days, so each day she does 1/8 of the job. If Clarissa works for x days, she will paint x/8 of the house.

Juan's part + Clarissa's part = whole job
(x/12) + (x/8) = 1

Now, solve that for x......

(NOTE.....the size of the house did not come into play here, since the house size remained the same whether they were working alone or together)

 

[JayJay06]

so my answer is 4 4/5 days

 

[Denis]

Correct.