Question 908581
Let {{{ t }}} = time in hrs for the train to
travel between the towns
{{{ t - 3/4 }}} = time in hrs for the bus
to travel between the towns
Let {{{ s }}} = the speed of the bus in km/hr
{{{ s - 15 }}} = the speed of the train in km/hr
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Equation for bus:
(1) {{{ 360 = s*( t - 3/4 ) }}}
Equation for train:
(2) {{{ 360 = ( s - 15 )*t }}}
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(1) {{{ 360 = s*t - (3/4)*s }}}
(1) {{{ 1440 = 4*s*t - 3s }}}
and
(2) {{{ t = 360/( s - 15 ) }}}
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Substitute (2) into (1)
(1) {{{ 1440 = 4*s*( 360 / ( s - 15 ) ) - 3s }}}
(1) {{{ 1440*( s - 15 ) = 1440s - 3s*( s - 15 ) }}}
(1) {{{ 1440s - 21600 = 1440s - 3s^2 + 45s }}}
(1) {{{ 3s^2 - 45s - 21600 = 0 }}}
(1) {{{ s^2 - 15s - 7200 = 0 }}}
use quadratic equation:
{{{ s = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -15 }}}
{{{ c = -7200 }}}
{{{ s = ( -(-15) +- sqrt( (-15)^2 - 4*1*(-7200) )) / (2*1) }}}
{{{ s = ( 15 +- sqrt( 225 + 28800 )) / 2 }}}
{{{ s = ( 15 +- sqrt( 29025 )) / 2 }}}
{{{ s = ( 15 + 170.367 ) / 2 }}}
{{{ s = 185.367 / 2 }}}
{{{ s = 92.684 }}}
the speed of the bus was 92.68 km/hr
check:
(2) {{{ 360 = ( s - 15 )*t }}}
(2) {{{ 360 = ( 92.68 - 15 )*t }}}
(2) {{{ 360 = 77.68t }}}
(2) {{{ t = 4.63 }}} hrs
and
(2) {{{ 360 = ( s - 15 )*t }}}
(2) {{{ 360 = ( 92.68 - 15 )*4.63 }}}
(2) {{{ 360 = 77.68*4.63 }}}
(2) {{{ 360 = 359.66 }}}
Looks close enough- error due
to rounding off