Question 760025
You can think of this problem with one of them, 
say David, standing still and Gloria approaching
David at the sum of their speeds.
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{{{ 47 + 47 + 5 = 99 }}} mi/hr = the sum of their speeds
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For the 1st 2 hrs, the sum of their speeds is
{{{ 47 + 0 = 47 }}}
{{{ d[1] = 47*2 }}}
{{{ d[1] = 94 }}} mi
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{{{ 391 - 94 = 297 }}}
Now for 297 miles the sum of their speeds is {{{ 99 }}} mi/hr
{{{ 297 = 99*t }}}
{{{ t = 3 }}} hrs
David left at 9 AM
Gloria left at 11 AM
3 hrs later they meet at 2 PM
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check answer:
David's equation:
{{{ d[2] = 47*( 2 + 3 ) }}}
{{{ d[2] = 235 }}} mi
Gloria's equation:
{{{ d[3] = 52*3 }}}
{{{ d[3] = 156 }}}
{{{ d[2] + d[3] = 235 + 156 }}}
{{{ d[2] + d[3] = 391 }}}
OK