Question 703368
Are you sure they're traveling in opposite directions?
It doesn't exactly say that. It just asks you for their
distance apart. I can solve it both ways, just in case.
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Traveling in opposite directions:
You have a 1 hour head start over brother.
{{{ d = 50*1 }}}
{{{ d = 50 }}} mi
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Now start a stop watch when your brother leaves
Let {{{ d[1] }}} = the distance he travels until noon
{{{ t = 3 }}} hrs
{{{ d[1] = 60*3 }}}
{{{ d[1] = 180 }}} mi
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Let {{{ d[2] }}} = your distance when stop watch starts
{{{ d[2] = 50*3 }}}
{{{ d[2] = 150 }}}
{{{ d[2] + 50 = 150 + 50 }}}
{{{ d[2] + 50 = 200 }}}
{{{ d[1] + d[2] + 50 = 180 + 150 + 50 }}}
{{{ d[1] + d[2] = 380  }}}
They are 380 mi apart at noon
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If they travel in the same direction:
Just subtract the distances
{{{ 200 - 180 = 20 }}}
They are 20 mi apart and you are ahead of brother