SOLUTION: two siblings-a brother and sister-attend the same school. Walking at constant rates the brother takes 40 minutes to walk home from school, while the sister only takes 30 minutes on

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Question 777031: two siblings-a brother and sister-attend the same school. Walking at constant rates the brother takes 40 minutes to walk home from school, while the sister only takes 30 minutes on the same route. If she leaves school 6 minutes after her brother, how many minutes has he traveled before she catches up to him?
I think it's 8 minutes but I just want to be sure. If it isn't 8, can you explain how to solve it? Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In +6+ minutes her brother has traveled
+6%2F40+=+3%2F20+ 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 ).
------------------
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+-+%283%2F20%29%2A120+=+%28+120%2F40+%29%2At+
Sister's equation:
(2) +d+=+%28+120%2F30+%29%2At+
---------------------
(1) +d+=+%283%2F20%29%2A120+%2B+%28+120%2F40+%29%2At+
By substitution:
(1) ++%28+120%2F30+%29%2At++=+%283%2F20%29%2A120+%2B+%28+120%2F40+%29%2At+
(1) +4t+=+18+%2B+3t+
(1) +t+=+18+
The brother has been traveling for +6+%2B+18+=+24+ min
------------
check:
(2) +d+=+%28+120%2F30+%29%2At+
(2) +d+=+%28+120%2F30+%29%2A18+
(2) +d+=+72+ mi
and
(1) +d+-+%283%2F20%29%2A120+=+%28+120%2F40+%29%2At+
(1) +d+-+%283%2F20%29%2A120+=+%28+120%2F40+%29%2A18+
(1) +d+-+18+=+54+
(1) +d+=+72+ mi
Hope I got it