Question

Sue did a job for $120. It took her 2 hours longer than she expected, and therefore she earned $2 per hour less than she anticipated.. How long did she expect that it would take to do the job?

Answer 1

Expected time to complete job `= 10` hours

Explanation:

Let
`color(white)("XXX")t_x=` expected time required
`color(white)("XXX")t_a =` actual time required
`color(white)("XXX")r_x=` expected rate of income
`color(white)("XXX")r_a=` actual rate of income

We are told
`color(white)("XXX")t_a=t_x+2`
`color(white)("XXX")r_a=r_x -2`

`r_x = 120/t_x` and `r_a=120/t_a = 120/(t_x+2)`

therefore
`color(white)("XXX")120/(t_x+2) = 120/t_x-2`

simplifying
`color(white)("XXX")120=(120(t_x+2))/(t_x)-2(t_x+2)`

`color(white)("XXX")cancel(120t_x) = cancel(120t_x)+240-2t_x^2-2t_x`

`color(white)("XXX")t_x^2+2t_x-120=0`

this factors as
`color(white)("XXX")(t_x+12)(t_x-10)=0`

and since `t_x > 0`
`rArr t_x = 10`