Question 777031
In {{{ 6 }}} minutes her brother has traveled
{{{ 6/40 = 3/20 }}} of the way home
The distance and the units are not given, so
I will say that the distance from school to home
is {{{ 120 }}} units of distance ( any units ).
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Let {{{ t }}} = the time in minutes it takes
sister to catch brother
Let {{{ d }}} = the distance sister travels until
she catches him
Brother's equation:
(1) {{{ d - (3/20)*120 = ( 120/40 )*t }}}  
Sister's equation:
(2) {{{ d = ( 120/30 )*t }}}
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(1) {{{ d = (3/20)*120 + ( 120/40 )*t }}}  
By substitution:
(1) {{{  ( 120/30 )*t  = (3/20)*120 + ( 120/40 )*t }}}  
(1) {{{ 4t = 18 + 3t }}}
(1) {{{ t = 18 }}}
The brother has been traveling for {{{ 6 + 18 = 24 }}} min
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check:
(2) {{{ d = ( 120/30 )*t }}}
(2) {{{ d = ( 120/30 )*18 }}}
(2) {{{ d = 72 }}} mi
and
(1) {{{ d - (3/20)*120 = ( 120/40 )*t }}}  
(1) {{{ d - (3/20)*120 = ( 120/40 )*18 }}}  
(1) {{{ d - 18 = 54 }}}
(1) {{{ d = 72 }}} mi
Hope I got it