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?

1 Answer
Alan P.
Oct 22, 2015

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#

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