Question 836360
Let {{{ s }}} = the car's average speed
(1) {{{ 432 = s*t }}}
(2) {{{ 432 = ( s+6 )*( t-1 ) }}}
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(1) {{{ s = 432/t }}}
and
(2) {{{ 432 = s*t + 6t - s - 6 }}}
(2) {{{ 432 + 6 = s*( t - 1 ) + 6t }}}
(2) {{{ 432 + 6 = (432/t)*( t - 1 ) + 6t }}}
(2) {{{ 438 = 432 - 432/t + 6t }}}
(2) {{{ 6 = -432/t + 6t }}}
(2) {{{ 6t = -432 + 6t^2 }}}
(2) {{{ 6t^2 - 6t - 432 = 0 }}}
(2) {{{ t^2 - t - 72 = 0 }}}
(2) {{{ ( t - 9 )*( t + 8 ) = 0 }}}
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Time can't be negative, so the answer is
{{{ t = 9 }}} hrs
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(1) {{{ 432 = s*t }}}
(1) {{{ 432 = s*9 }}}
(1) {{{ s = 48 }}}
The average speed is 48 mi/hr
check:
(2) {{{ 432 = ( s+6 )*( t-1 ) }}}
(2) {{{ 432 = ( 48+6 )*( 9-1 ) }}}
(2) {{{ 432 = 54*8 }}}
(2) {{{ 432 = 432 }}}
OK