SOLUTION: a plane left an airport at 4PM flying west at the rate of 300MPH. AT 4:30PM another plane left the same airport, flying west at the rate of 350 MPH. at what time did the second pl

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Question 992952: a plane left an airport at 4PM flying west at the rate of 300MPH. AT 4:30PM another plane left the same airport, flying west at the rate of 350 MPH. at what time did the second plane overtake the first plane?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What was the 1st plane's head start in miles?
+d%5B1%5D+=+300%2A%281%2F2%29+
+d%5B1%5D+=+150+ mi
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Start a stopwatch when the 2nd plane leaves
Let +t+ = time in hrs on stopwatch when
2nd plane catches 1st plane.
Let +d+ = distance the 2nd plane travels
until it catches 1st plane
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1st plane's equation:
(1) +d+-+150+=+300%2At+
2nd plane's equation:
(2) +d+=+350t+
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Substitute (2) into (1)
(1) +350t+-+150+=+300t+
(1) +50t+=+150+
(1) +t+=+3+ hrs
+3+ hrs past 4:30 is 7:30 PM when
2nd plane catches 1st
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check:
(2) +d+=+350t+
(2) +d+=+350%2A3+
(2) +d+=+1050+
and
(1) +d+-+150+=+300%2At+
(1) +d+-+150+=+300%2A3+
(1) +d+=+150+%2B+900+
(1) +d+=+1050+
OK