Question 710809
In order for Roberto to overtake Juanita, he has to be the faster walker.
Walking in the same direction:
Let {{{ d }}} = the distance Roberto travels until he catches Juanita
{{{ d - 4.4 }}} = the distance Juanita travels when Roberto catches her
Let {{{ r }}} = Roberto's speed
Let {{{ s }}} = Juanita's speed
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Roberto's equation:
(1) {{{ d = r*11 }}}
Juanita's equation:
(2) {{{ d - 4.4 = s*11 }}}
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Walking towards each other:
They approach each other at the sum of their speeds, and
together, they cover {{{ 4.4 }}} mi
{{{ 4.4 = ( r + s )*1 }}} 
(3) {{{ r + s = 4.4 }}}
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Substitute (1) into (2)
(2) {{{ 11r - 4.4 = s*11 }}}
(2) {{{ 11r - 11s = 4.4 }}}
(2) {{{ r - s = .4 }}}
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Add equations (2) and (3)
(3) {{{ r + s = 4.4 }}}
(2) {{{ r - s = .4 }}}
{{{ 2r = 4.8 }}}
{{{ r = 2.4 }}}
and, since
(3) {{{ r + s = 4.4 }}}
(3) {{{ 2.4 + s = 4.4 }}}
(3) {{{ s = 2 }}}
Roberto's speed is 2.4 mi/hr
Juanita's speed is 2 mi/hr