Question 1150319
Let {{{ r }}} = his normal  rate in mi/hr
Let {{{ t }}} = his normal time in hrs
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Normal rate:
(1) {{{ 24 = r*t }}}
Faster rate:
(2) {{{ 24 = ( r + 6 )*( t - 9 ) }}}
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(1) {{{ t = 24/r }}}
(2) {{{ 24 = ( r + 6 )*( 24/r - 9 ) }}}
(2) {{{ 24 = 24 + 144/r - 9r - 54 }}}
(2) {{{ 0 = 144/r - 9r - 54 }}}
(2) {{{ 144/r = 9r + 54 }}}
(2) {{{ 144 = 9r^2 + 54r }}}
(2) {{{ 16 = r^2 + 6r }}}
(2) {{{ r^2 + 6r - 16 = 0 }}}
(2) {{{ ( r + 8 )*( r - 2 ) = 0 }}}
(2) {{{ r = 2 }}} ( can't use the negative result )
His normal rate was 2 mi/hr
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check answer:
(1) {{{ 24 = r*t }}}
(1) {{{ 24 = 2*t }}}
(1) {{{ t = 12 }}} hrs
and
(2) {{{ 24 = ( r + 6 )*( t - 9 ) }}}
(2) {{{ 24 = ( 2 + 6 )*( t - 9 ) }}}
(2) {{{ 24 = 8*( t - 9 ) }}}
(2) {{{ t - 9 = 3 }}}
(2) {{{ t = 12 }}}
OK