Question 1084609
(1)
Time for ordinary train:
{{{ 300 / x }}}
Time for express train:
{{{ 300 / x + 25 }}}
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(2)
{{{ 300/x = 300/( x + 25 ) + 2 }}}
Multiply both sides by {{{ x*( x + 25 ) }}}
{{{ 300*( x + 25 ) = 300x + 2*x*( x + 25 ) }}}
{{{ 300x + 7500 = 300x + 2x^2 + 50x }}}
{{{ 2x^2 + 50x - 7500 = 0 }}}
{{{ x^2 + 25x - 3750 = 0 }}}
Use quadratic formula
{{{ x = ( -b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = 25 }}}
{{{ c = -3750 }}}
{{{ x = ( -25 +- sqrt( 25^2-4*1*(-3750) ))/(2*1) }}}
{{{ x = ( -25 +- sqrt( 625 + 15000 ))/2 }}}
{{{ x = ( -25 +- sqrt( 15625 ))/2 }}}
{{{ x = ( -25 + 125 ) / 2 }}} ( can't use the negative sqrt )
{{{ x = 100/2 }}}
{{{ x = 50 }}} 
and
{{{ x + 25 = 75 }}}
The speed of the express train is 75 km/hr
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check:
{{{ 300/x = 300/( x + 25 ) + 2 }}}
{{{ 300/50 = 300/75 + 2 }}}
Multiply both sides by {{{ 150 }}}
{{{ 3*300 = 2*300 + 300 }}}
{{{ 900 = 600 + 300 }}}
{{{ 900 = 900 }}}
OK