Question 764730
What was Michael's head start in miles?
He had a {{{ 4 }}} hr head start  ( 6AM to 10AM )
{{{ d[1] = 30*4 }}}
{{{ d[1] = 120 }}} miles head start
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Ruth leaves the same exit and
{{{ 4 }}} hrs later, ( 10AM to 2PM ), she is {{{ 16 }}} mi
ahead of michael
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Let {{{ d }}} = distance Ruth travels from 10AM to 2 PM
{{{ d - 16 }}} = distance Michael travels from 10AM to 2 PM
Let {{{ s }}} = Ruth's average speed 
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Ruth's equation:
(1) {{{ d  = s*4 }}}
Michael's equation:
(2) {{{ ( d - 16 ) - 120 = 30*4 }}}
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(2) {{{ d - 136 = 120 }}}
(2) {{{ d = 256 }}}
and
(1) {{{ d = 4s }}}
(1) {{{ 256 = 4s }}}
(1) {{{ s = 64 }}}
Ruth's average speed is 64 mi/hr
check:
Michael should go {{{ 256 - 16 = 240 }}} mi
in {{{ 4 + 4  = 8 }}} hrs
{{{ d[2] = 30*8 }}}
{{{ d[2] = 240 }}} mi
OK