Question

Working together, it takes Sam, Jenna, and Francisco two hours to paint one room. When Sam works alone, he can paint one room in 6 hours. When Jenna works alone, she can paint one room in 4 hours. Determine how long it would take Francisco to paint one room on his own.

Answer 1

Answer: 12 hours

Explanation:

Given : Working together, it takes Sam, Jenna, and Francisco two hours to paint one room.

When Sam works alone, he can paint one room in 6 hours. When Jenna works alone, she can paint one room in 4 hours.

Let 't' be the time taken by Francisco to paint one room on his own.

Then , we have

Rate of work of Sam +Rate of work of Jenna + Rate of work of Francisco =Rate of work they all do together

`(1)/(6)+(1)/(4)+(1)/(t)=(1)/(2)`

i.e.
`(1)/(t)=(1)/(2)-((1)/(6)+(1)/(4))`

i.e.
`(1)/(t)=(1)/(2)-((4+6)/(24))`

i.e.
`(1)/(t)=(1)/(2)-(10)/(24)`

i.e.
`(1)/(t)=(1)/(2)-(5)/(12)`

i.e.
`(1)/(t)=(6-5)/(12)`

i.e.
`(1)/(t)=(1)/(12)`

i.e. t= 12

Hence, Francisco would take 12 hours to paint one room on his own.