Question 878872
Let {{{ r[1] }}} = her ave rate going to mountains in mi/hr
Let {{{ r[2] }}} = her ave rate driving back in mi/hr
Let {{{ d }}} = the one-way distance to mountains
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(1) {{{ r[2] = r[1] + 16 }}}
(2) {{{ r[1] = d / 8 }}}
(3) {{{ r[2] = d / 6 }}}
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Substitute (2) and (3) into (1)
(1) {{{ d/6 = d/8 + 16 }}}
Multiply both sides by {{{ 24 }}}
(1) {{{ 4d = 3d + 16*24 }}} 
(1) {{{ d = 16*24 }}}
(1) {{{ d = 16*24 }}}
(1) {{{ d = 384 }}}
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(2) {{{ r[1] = 384 / 8 }}}
(2) {{{ r[1] = 48 }}} mi/hr
and
(1) {{{ r[2] = 384 / 6 }}}
(1) {{{ r[2] = 64 }}} mi/hr
Her ave rate going to mountains was 48 mi/hr
Her ave rate driving back was 64 mi/hr
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check:
(1) {{{ r[2] = r[1] + 16 }}}
(1) {{{ 64 = 48 + 16 }}}
(1) {{{ 64 = 64 }}}
OK