SOLUTION: A plane leaves Chicago flying due east at 225 mph. While a train that left 2 1/4 hours earlier is going due east at 85 mph. How much time will it take them to be 750 miles apart

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Question 879274: A plane leaves Chicago flying due east at 225 mph. While a train that left 2 1/4 hours earlier is going due east at 85 mph. How much time will it take them to be 750 miles apart?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What is the train's head start?
+d%5B1%5D+=+85%2A2.25+
+d%5B1%5D+=+191.25+ mi
----------------------
Let +d+ = the distance the plane travels
when they are +750+ mi apart
Let +t+ = the time that the plane travels
when they are +750+ mi apart
--------------------------------
Plane's equation:
(1) +d+=+225t+
Train's equation:
(2) +%28+d+-+191.25+%29+-+750+=+85t+
-------------------------------
(2) +d+-+941.25+=+85t+
Substitute (1) into (2)
(2) +225t+-+941.25+=+85t+
(2) +140t+=+941.25+
(2) +t+=+6.7232+
also +.7232%2A60+=+43+
It will take them 6 hrs and 43 min
check:
(1) +d+=+225t+
(1) +d+=+225%2A6.7232+
(1) +d+=+1512.72+
and
(2) +%28+d+-+191.25+%29+-+750+=+85t+
(2) +%28+d+-+191.25+%29+-+750+=+85%2A6.7232+
(2) +d+-+941.25+=+571.472+
(2) +d+=+1512.72+
OK