Question 695748
Start a stopwatch when his sister leaves. 
In miles, the boy has a {{{ 9*( 1/6) = 1.5 }}} mi head start
Let {{{ d }}} = the distance the sister has to travel until
she catches her brother
Let {{{ t }}} = time on stopwatch when she catches him
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Sister's equation:
(1) {{{ d = 12t }}}
Brother's equation:
(2) {{{ d - 1.5 = 9t }}}
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Substitute (1) into (2)
(2) {{{ 12t - 1.5 = 9t }}}
(2) {{{ 3t = 1.5 }}}
(2) {{{ t = .5 }}}
It takes her 1/2 hr to catch her brother
check:
(1) {{{ d = 12*.5 }}}
(1) {{{ d = 6 }}}
and
(2) {{{ d - 1.5 = 9*.5 }}}
(2) {{{ d = 4.5 + 1.5 }}}
(20 {{{ d = 6 }}}
OK