Question 1004689
Let {{{ d }}} = the distance each one travels in miles
Let {{{ t }}} = the time in hours it takes for the man
to reach the point where his wife catches up
{{{ t - 1 }}} = time in hours for wife to catch man
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Man's equation:
{{{ d = 45t }}}
Wife's equation:
{{{ d = 55*( t-1 ) }}}
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By susbstitution:
{{{ 45t = 55*( t-1 ) }}}
{{{ 45t = 55t - 55 }}}
{{{ 10t = 55 }}}
{{{ t = 5.5 }}}
and
{{{ t - 1 = 4.5 }}}
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The man travels for 5.5 hrs
His wife travels for 4.5 hrs
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check:
{{{ d = 45t }}}
{{{ d = 45*5.5 }}}
{{{ d = 247.5 }}}
and
{{{ d = 55*( t-1 ) }}}
{{{ d = 55*4.5 }}}
{{{ d = 247.5 }}}
OK