SOLUTION: Ben starts walking along a path at 2 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 4 mi/h. How long will it be before Amanda

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Question 1015573: Ben starts walking along a path at 2 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 4 mi/h. How long will it be before Amanda catches up to Ben?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What is Ben's head start in miles?
+d%5B1%5D+=+2%2A1.5+
+d%5B1%5D+=+3+ mi
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Let +d+ = distance Amanda travels
until she catches up to Ben
Start a stop watch when Amanda leaves
Let +t+ = time on stopwatch when
she catches up with Ben
---------------------
Ben's equation
(1) +d+-+3+=+2t+
Amanda's equation:
(2) +d+=+4t+
----------------
Substitute (2) into (1)
(1) +4t+-+3+=+2t+
(1) +2t+=+3+
(1) +t+=+3%2F2+
She catches up to Ben in 1.5 hrs
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check:
(2) +d+=+4t+
(2) +d+=+4%2A1.5+
(2) +d+=+6+ mi
and
(1) +d+-+3+=+2t+
(1) +d+-+3+=+2%2A1.5+
(1) +d+-+3+=+3+
(1) +d+=+6+
OK