Jesse and Leah can install a new gutter system on a house in 4 hours when they work

Question

together. Working alone, it would take Leah twice as long to install a new gutter system
as it would take Jesse working by himself. Leah caught a really bad cold and called in
sick this morning. How long will it take Jesse to install a new gutter system on a house
by himself?

Answer 1

let the time taken by Jesse be x hrs
then the time taken by Leah is 2x hrs

then Jesse's rate is 1/x jobs/hr
and Leah's rate is 1/2x jobs/hr

combined rate = 1/x + 1/2x
= (3/(2x))

but 1/(3/2x) = 4
1 = 4(3/2x)
2x = 12
x = 6

It would take Jesse 6 hrs to do the job alone, and it would take Leah 12 hrs to do the job alone