Question 1032239
Let {{{ c }}} = the plumber's charge/hr
Let {{{ t }}} = time in hours the plumber worked
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Plumber's equation:
(1) {{{ c = 600/t }}}
Apprentice's equation:
(2) {{{ c - 3 = 600/( t + 10 ) }}}
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Substitute (1) into (2)
(2) {{{ 600/t - 3 = 600/( t + 10 ) }}}
Multiply both sides by {{{ t*( t + 10 ) }}}
(2) {{{ 600*( t + 10 ) - 3*t*( t + 10 ) = 600t }}}
(2) {{{ 600t + 6000 - 3t^2 - 30t = 600t }}}
(2) {{{ 3t^2 + 30t - 6000 = 0 }}}
(2) {{{ t^2 + 10t - 2000 = 0 }}}
I note that {{{ 2000 = 40*50 }}}
(2) {{{ ( t + 50 )*( t - 40 ) }}}
{{{ t = 40 }}}
and
(1) {{{ c = 600/t }}}
(1) {{{ c = 600/40 }}}
(1) {{{ c = 15 }}}
The plumber made $15/hr
( this must be on some other planet! )
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check:
(2) {{{ c - 3 = 600/( t + 10 ) }}}
(2) {{{ 15 - 3 = 600/( 40 + 10 ) }}}
(2) {{{ 12 = 600/50 }}}
(2) {{{ 12 = 12 }}}
OK