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