Question 1027022
I think the key to this problem is that the student
took the job for a FLAT RATE of $48.
If he was being paid hourly at a fixed HOURLY rate
and took longer, he would have made more, not less
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Let {{{ t }}} = time in hours he expected
it would take to do the job
{{{ t + 8 }}} = time in hours it actually 
took him to do the job
Let {{{ r }}} = hourly rate in dollars he
expected to be paid for the job
{{{ r - 3 }}} = hourly rate  in dollars that
he actually got paid for the job
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Equation for what he expected would happen:
(1) {{{ r*t = 48 }}}
Equation for what actually happened:
(2) {{{ ( r - 3 )*( t + 8 ) = 48 }}}
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(2) {{{ r*t - 3t + 8r - 24 = 48 }}}
(2) {{{ r*( t + 8 ) - 3t = 72 }}}
and
(1) {{{ r = 48/t }}}
Substitute (1) into (2)
(2) {{{ (48/t)*( t + 8 ) - 3t = 72 }}}
(2) {{{ 48*( t + 8 ) - 3t^2 = 72t }}}
(2) {{{ 48t + 384 - 3t^2 = 72t }}}
(2) {{{ 3t^2 + 24t - 384 }}}
(2) {{{ t^2 + 8t - 128 = 0 }}}
I notice that {{{ 128 = 8*16 }}} and
{{{ 16 - 8 = 8 }}}, so I can guess that:
(2) {{{ ( t + 16 )*( t - 8 ) = 0 }}}
Time has to be positive, so {{{ t = 8 }}}
He expected to finish the job in 8 hrs
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check:
(1) {{{ r*t = 48 }}}
(1) {{{ r*8 = 48 }}}
(1) {{{ r = 6 }}} dollars/hr
and
(2) {{{ ( r - 3 )*( t + 8 ) = 48 }}}
(2) {{{ ( r - 3 )*( 8 + 8 ) = 48 }}}
(2) {{{ ( r - 3 )*16 = 48 }}}
(2) {{{ r - 3 = 3 }}}
(2) {{{ r = 6 }}} dollars/hr
OK