Question 662409
You can think of one of them ( either one )
as standing still and the other approaching
at the sum of their speeds.
Let {{{ t }}} = elapsed time in hrs until they meet
{{{ 19 = ( 5 + 8 )*t }}}
{{{ 19 = 13t }}}
{{{ t = 19/13 }}} hrs
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David's equation:
{{{ d = 5*(19/13) }}}
{{{ d = 95/13 }}}
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Alex's equation:
{{{ d = 8*(19/13) }}}
{{{ d = 152/13 }}}
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David is 95/13 km from his home
Alex is 152/13 km from his home
check:
{{{ (13/13)*19 = 247/13 }}}
{{{ 95/13 + 152/13 = 247/13 }}}
OK