Question 683843
Let {{{s }}} = his speed in km/hr
{{{ s + 5 }}} = his speed plus {{{ 5 }}} km/hr
Let {{{ t }}} = his time to travel 156 km
{{{ t - 12/60 }}} his time minus {{{ 12 }}} min 
as fraction of an hour
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Equation for actual trip:
(1) {{{ 156 = s*t }}}
Equation for 5 km/hr faster:
(2) {{{ 156 = ( s + 5 )*( t - 1/5 ) }}}
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(2) {{{ 156 = s*t + 5t - (1/5)*s - 1 }}}
and
(1) {{{ t = 156/s }}}
Substitute (1) into (2)
(2) {{{ 156 = s*( 156/s ) + 5*( 156/s ) - (1/5)*s - 1 }}}
(2) {{{ 156 = 156 + 780/s  - (1/5)*s - 1 }}}
(2) {{{ 0 = 780/s  - (1/5)*s - 1 }}}
(2) {{{ 1 = 780/s  - (1/5)*s  }}}
Multiply both sides by {{{ 5s }}}
(2) {{{ 5s = 3900 - s^2 }}}
(2) {{{ s^2 + 5s - 3900 = 0 }}}
Use quadratic equation:
{{{ s = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = 5 }}}
{{{ c = -3900 }}}
{{{ s = (-5 +- sqrt( 5^2 - 4*1*(-3900) )) / (2*1) }}}
{{{ s = (-5 +- sqrt( 25 + 15600 )) / 2 }}}
{{{ s = (-5 +- sqrt( 15625 )) / 2 }}}
{{{ s = (-5 + 125) / 2 }}} ( ignore the negative square root )
{{{ s = 120/2 }}}
{{{ s = 60 }}}
His speed was 60 km/hr
check:
(1) {{{ 156 = 60*t }}}
(1) {{{ t = 156/60 }}}
(1) {{{ t = 2.6 }}}
and
(2) {{{ 156 = ( 60 + 5 )*( 2 + 3/5 - 1/5 ) }}}
(2) {{{ 156 = 65*( 2 + 2/5 ) }}}
(2) {{{ 156 = 130 + 26 }}}
(2) {{{ 156 = 156 }}}
OK