Question 969347
Let {{{ s }}} = her normal speed in mi/hr
{{{ s + 7 }}} = her faster speed in mi/hr
Let {{{ t }}} = her time in hours 
when traveling at {{{ s }}} mi/hr
{{{ t - 1 }}} = her time in hours when
traveling at {{{ s + 7 }}} mi/hr
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Equation for traveling at normal speed
(1) {{{ 770 = s*t }}}
Equation for traveling at faster speed
(2) {{{ 770 = ( s+7 )*( t - 1 ) }}}
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(2) {{{ 770 = s*t + 7t - s - 7 }}}
and
(1) {{{ s = 770/t }}}
(2) {{{ 770 = ( 770/t )*t + 7t - 770/t - 7 }}}
(2) {{{ 770 = 770 + 7t - 770/t - 7 }}}
(2) {{{ 0 = 7t - 770/t - 7 }}}
(2) {{{ 770/t  = 7t - 7 }}}
Multiply both sides by {{{ t }}}
(2) {{{ 770 = 7t^2 - 7t }}}
(2) {{{ 7t^2 - 7t - 770 = 0 }}}
(2) {{{ t^2 - t - 110 = 0 }}}
(2) {{{ ( t - 11 )*( t + 10 ) }}} ( by looking at it )
{{{ t = 11 }}} ( time must be positive )
and
(1) {{{ s = 770/t }}}
(1) {{{ s = 770/11 }}}
(1) {{{ s = 70 }}}
the average speed is 70 mi/hr
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check:
(2) {{{ 770 = ( s+7 )*( t - 1 ) }}}
(2) {{{ 770 = ( 70+7 )*( 11 - 1 ) }}}
(2) {{{ 770 = 77*10 }}}
(2) {{{ 770 = 770 }}}
OK