Question

Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?

a) 1/3x
b) 3x/x-3
c) x-3/3x
d) x/x-3
e) x-3/x

Answer 1

`(x-3)/(3x)`

Explanation:

Lindsay can paint 1/x of a certain room in 20 minutes.

1 hour = 3 times 20 minutes

rate of work by Lindsay in 20 minutes is
`(3)/(x)`

Let 't' be the work done by Joseph

rate of work by Joseph in 20 minutes is
`(3)/(t)`

Both completed the work in 1 hour

`(3)/(x) +(3)/(t) =1`

solve the equation for 't'

Subtract 3/x on both sides

`(3)/(t) =1-(3)/(x)`

`(3)/(t) =(x-3)/(x)`

cross multiply it

`3x=t(x-3)`

Divide both sides by x-3

`(3x)/(x-3) =t`

Work done together is

`(x-3)/(3x)`