Question 883786
Let {{{ d }}} = the one-way distance 
in miles to her mother's house
Let {{{ s }}} = her average speed in mi/hr on Sat.
{{{ s - 7 }}} = her average speed in mi/hr on Sun.
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Equation for Sat:
(1) {{{ d = s*4.5 }}}
Equation for Sun:
(2) {{{ d = ( s - 7 )*5 }}}
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By substitution:
{{{ 4.5s = ( s - 7 )*5 }}}
{{{ 4.5s = 5s - 35 }}}
{{{ .5s = 35 }}}
{{{ s = 35/.5 }}}
{{{ s = 70  }}}
{{{ s - 7 = 63 }}}
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Her average speed on Sun was 63 mi/hr
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check:
(1) {{{ d = s*4.5 }}}
(1) {{{ d = 70*4.5 }}}
(1) {{{ d = 315 }}} mi
and
(2) {{{ d = ( s - 7 )*5 }}}
(2) {{{ d = 63*5 }}}
(2) {{{ d = 315 }}} mi
OK