Question 980585
Average speed is always [ total distance ] / [ total time ]
Let {{{ d }}} = distance in miles between New Orleans and Boston
Let {{{ t }}} = time in hrs going from New Orleans to Boston
{{{ t - 1 }}} = time in hrs going from Boston to New Orleans
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Equation for New Orleans to Boston:
(1) {{{ d = 40t }}}
Equation for Boston to New Orleans:
(2) {{{ d = 80*( t-1 ) }}}
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[ total distance ] = {{{ 2d }}}
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(1) {{{ t = d/40 }}}
(2) {{{ d = 80*( t-1) }}}
(2) {{{ t-1 = d/80 }}}
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[ total time ] = {{{ t + t-1 = d/40 + d/80 }}}
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[ total distance ] / [ total time ] = {{{ ( 2d ) / ( d/40 + d/80 ) }}} 
Divide top and bottom by {{{ d }}}
{{{ 2 / ( 1/40 + 1/80 ) }}}
Multiply top and bottom by {{{ 80 }}}
{{{ 160 / ( 2 + 1 ) = 53.333 }}} mi/hr
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Note that you do not take the average of the two averages
which would be: {{{ ( 40 + 80 ) / 2 = 60 }}} mi/hr