Question 550389
Let {{{s}}} = speed of express train
{{{ s - 12 }}} = speed of slower train
Let {{{ t }}} = time for express train to cover {{{ 240 }}} km
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Express train:
(1) {{{ 240 = s*t }}}
Slower train:
(2) {{{ 240 = ( s - 12 )*( t + 1 ) }}}
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(2) {{{ 240 = s*t - 12t + s - 12 }}}
Substitute (1) into (2)
(2) {{{ s*t = s*t - 12t + s - 12 }}}
(2) {{{ 12t = s - 12 }}}
(2) {{{ t = (1/12)*s - 1 }}}
Substitute this into (1)
(1) {{{ 240 = s*( (1/12)*s - 1 ) }}}
(1) {{{ 240 = (1/12)*s^2 - s }}}
(1) {{{ 2880 = s^2 - 12s }}}
(1) {{{ s^2 - 12s = 2880 }}}
Complete the square
(1) {{{ s^2 - 12s + (12/2)^2 = 2880 + (12/2)^2 }}}
(1) {{{ s^2 - 12s + 36 = 2880 + 36 }}}
(1) {{{ ( s - 6 )^2 = 2916 }}}
(1) {{{ ( s - 6 )^2 = 54^2 }}}
(1) {{{ s - 6 = 54 }}}
(1) {{{ s = 60 }}}
The speed of the express train is 60 km/hr
check answer:
(1) {{{ 240 = s*t }}}
(1) {{{ 240 = 60t }}}
(1) {{{ t = 4 }}} hrs
and
(2) {{{ 240 = ( 60 - 12 )*( t + 1 ) }}}
(2) {{{ 240 = 48*( t + 1 ) }}}
(2) {{{ 240 = 48t + 48 }}}
(2) {{{ 48t = 192 }}}
(2) {{{ t = 4 }}} hrs
OK