Question 919187
Let {{{ s }}} = Bianca's average speed
Let {{{ t }}} = her time in hrs to travel 1200nkm
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(1) {{{ 1200 = s*t }}}
(2) {{{ 1200 = ( s+5 )*( t - 12 ) }}}
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(2) {{{ 1200 = s*t + 5t - 12s - 60 }}}
(2) {{{ 1200 = t*( s+5 ) - 12s - 60 }}}
and
(1) {{{ t = 1200/s }}}
(2) {{{ 1200 = ( 1200/s )*( s+5 ) - 12s - 60 }}}
(2) {{{ 1200 = 1200 + 6000/s - 12s - 60 }}}
(2) {{{ 6000/s = 12s + 60 }}}
(2) {{{ 6000 = 12s^2 + 60s }}}
(2) {{{ s^2 + 5s = 500 }}}
Complete the square
(2) {{{ s^2 + 5s + (5/2)^2 = 500 + (5/2)^2 }}}
(2) {{{ s^2 + 5s + 25/4 = 500 + 25/4 }}}
(2) {{{ ( s + 5/2 )^2 = 2025/4 }}}
(2) {{{ ( s + 5/2 )^2 = ( 45/2 )^2 }}}
Take the square root of both sides
(2) {{{ s + 5/2 = 45/2 }}} ( only the positive root works here )
(2) {{{ s = 40/2 }}}
(2) {{{ s = 20 }}}
Her average speed is 20 km/hr
check:
(1) {{{ t = 1200/s }}}
(1) {{{ t = 1200/20 }}}
(1) {{{ t = 60 }}}
and
(2) {{{ 1200 = ( s+5 )*( t - 12 ) }}}
(2) {{{ 1200 = ( 20+5 )*( 60 - 12 ) }}}
(2) {{{ 1200 = 25*48 }}}
(2) {{{ 1200 = 1200 }}}
OK