SOLUTION: A boy is biking home from school at 9 miles per hour. He is 10 minutes ahead of his sister who is biking at 12 miles per hour. How long will it take for the sister to catch up with

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Question 695748: A boy is biking home from school at 9 miles per hour. He is 10 minutes ahead of his sister who is biking at 12 miles per hour. How long will it take for the sister to catch up with her brother?
I tried using the equation 12x=9x + 1/6 (because 10 minutes is 1/6 of an hour) the answer I got was 1/9 but it wasn't one of the choices.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Start a stopwatch when his sister leaves.
In miles, the boy has a +9%2A%28+1%2F6%29+=+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
--------------------
Sister's equation:
(1) +d+=+12t+
Brother's equation:
(2) +d+-+1.5+=+9t+
------------------
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%2A.5+
(1) +d+=+6+
and
(2) +d+-+1.5+=+9%2A.5+
(2) +d+=+4.5+%2B+1.5+
(20 +d+=+6+
OK