Question 1120901
Let s[A] = train A痴 speed
Let s[B] = train B痴 speed
Let t = time in hrs for them to meet
{{{ s[A]*t }}} = distance A travels until they meet
{{{ s[B]*t }}} = distance B travels until they meet
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You are given that
{{{ s[A]*( t + 9 ) = 300 }}}
{{{ s[B]*( t + 4 ) = 300 }}}
{{{ s[A]*t + s[B]*t = 300 }}}
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{{{ s[A] = 300/( t + 9 ) }}}
{{{ s[B] = 300/( t + 4 ) }}}
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{{{ 300t/ ( t + 9 ) + 300t /( t + 4 ) = 300 }}}
{{{ t/( t + 9 ) + t/( t + 4 ) = 1 }}}
multiply both sides by {{{ ( t + 9 )*( t + 4 ) }}}
{{{ t*( t + 4 ) + t*( t + 9 ) = ( t + 4 )*( t + 9 ) }}}
{{{ t^2 + 4t + t^2 + 9t = t^2 + 4t + 9t + 36 }}}
{{{ t^2 = 36 }}}
{{{ t = 6 }}}
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{{{ s[A] = 300/( 6 + 9 ) }}}
{{{ s[A] = 20 }}} km/hr
And
{{{ s[B] = 300/( 6 + 4 ) }}}
{{{ s[B] = 30 }}} km/hr