Question 771246
Let {{{ d }}} = the distance the slower train travels in km
{{{ d + 40 }}} = the distance the faster train travels in km
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{{{ d = 40t }}}
{{{ d + 40 = 45t }}}
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{{{ t = d/40 }}}
By substitution:
{{{ d + 40 = 45*( d/40 ) }}}
{{{ 40d + 1600 = 45d }}}
{{{ 5d = 1600 }}}
{{{ d = 320 }}}
The distance between the stations is
{{{ d + d + 40 = 320 + 320 + 40 }}}
{{{ 2d + 40 = 680 }}}
680 km
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check:
{{{ d = 40t }}}
{{{ 320 = 40t }}}
{{{ t = 8 }}}
and
{{{ d + 40 = 45t }}}
{{{ 320 + 40 = 45t }}}
{{{ 45t = 360 }}}
{{{ t = 8 }}}
OK