Question 833264
The sum of the distances they walk 
has got to add up to 19 mi
Let {{{ d }}} = the distance the slower hiker travels in miles
{{{ 19 - d }}} = the distance the faster hiker travels in miles
Let {{{ s }}} = the slower hiker's speed in mi/hr
{{{ s + .5 }}} = the faster hiker's speed in mi/hr
The time is {{{ 2 }}} hrs for both hikers
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Equation for the slower hiker:
(1) {{{ d = s*2 }}}
Equation for faster hiker:
(2) {{{ 19 - d = ( s+.5 )*2 }}}
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Substitute (1) into (2)
(2) {{{ 19 - 2s = ( s+.5 )*2 }}}
(2) {{{ 19 - 2s = 2s + 1 }}}
(2) {{{ 4s = 18 }}}
(2) {{{ s = 4.5 }}} mi/hr
and
{{{ s + .5 = 5 }}} mi/hr
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The slower hiker's speed is 4.5 mi/hr
The faster hiker's speed is 5 mi/hr
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check:
(2) {{{ 19 - d = ( s+.5 )*2 }}}
(2) {{{ 19 - d = 5*2 }}}
(2) {{{ d = 9 }}} mi
and
(1) {{{ d = s*2 }}}
(1) {{{ d = 4.5*2 }}}
(1) {{{ d = 9 }}} mi
OK