Question 1029799
Let {{{ d }}} = distance in miles
Let {{{ r }}} = average rate in mi/hr
Let {{{ t }}} = time in hrs
{{{ d = r*t }}}
{{{ t = d/r }}}
{{{ t = 120 / r }}}
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also given:
{{{ t= 136 / ( r + 6 ) }}}
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The times were the same, so
{{{ 120/r = 136/( r + 6 ) }}}
Multiply both sides by {{{ r*( r + 6 ) }}}
{{{ 120*( r + 6 ) = 136r }}}
{{{ 120r + 720 = 136r }}}
{{{ 16r = 720 }}}
{{{ r = 45 }}}
The mean speed was 45 mi/hr
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check:
{{{ t = 120 / r }}}
{{{ t = 120 / 45 }}}
{{{ t = 2.667 }}} hrs
and
{{{ t= 136 / ( r + 6 ) }}}
{{{ t= 136 / ( 45 + 6 ) }}}
{{{ t = 136 / 51 }}}
{{{ t = 2.667 }}} hrs
OK