Question

Dominic spent hours on his art project. Rachel worked times as long on her art project as Dominic worked. For how many hours did Rachel work on her art project?

Answer 1

Rachel worked for
`3(2)/(3)` hours

Explanation:

See comment for complete question

Given

Let

`D = Dominic`

`R = Rachel`

So:

`D = 2(3)/(4)`

and

`R =1(1)/(3)` as long as D

Required

Determine the number of hours spent by Rachel

This implies that:

`R =1(1)/(3)` as long as D

Rewrite as:

`R =1(1)/(3) * D`

Substitute:
`D = 2(3)/(4)`

`R =1(1)/(3) * 2(3)/(4)`

Express as improper fraction

`R =(4)/(3) * (11)/(4)`

This gives:

`R =(1)/(3) * 11`

`R =(11)/(3)`

Express as mixed numbers

`R =3(2)/(3)`

Hence, Rachel worked for
`3(2)/(3)` hours