SOLUTION: A commuter plane provides transportation from an international airport to the surrounding cities. One commuter plane averaged 280 mph flying to a city and 120 mph returning to the

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Question 876731: A commuter plane provides transportation from an international airport to the surrounding cities. One commuter plane averaged 280 mph flying to a city and 120 mph returning to the international airport. The total flying time was 4 h. Find the distance between the two airports.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Time in hrs flying to the city:
(1) +t%5B1%5D+=+d+%2F+280+
Time in hrs flying back:
(2) +t%5B2%5D+=+d+%2F+120+
------------------
(3) +t%5B1%5D+%2B+t%5B2%5D+=+4+
-----------------
(1) +d+=+280t%7B1%5D+
(2) +d+=+120t%5B2%5D+
Subtract (2) from (1)
+280t%5B1%5D+=+120t%5B2%5D+
+t%5B2%5D+=+%28+7%2F3+%29%2At%5B1%5D+
--------------------
By substitution:
(3) +t%5B1%5D+%2B+%28+7%2F3+%29%2At%5B1%5D+=+4+
(3) +%28+10%2F3+%29%2At%5B1%5D+=+4+
(3) +t%5B1%5D+=+%283%2F10%29%2A4+
(3) +t%5B1%5D+=+1.2+ hrs
and
+t%5B2%5D+=+%28+7%2F3+%29%2At%5B1%5D+
+t%5B2%5D+=+%28+7%2F3+%29%2A%286%2F5%29+
+t%5B2%5D+=+42%2F15+
+t%5B2%5D+=+2.8+
and
(1) +d+=+280t%7B1%5D+
(1) +d+=+280%2A1.2+
(1) +d+=+336+
check:
(2) +d+=+120t%5B2%5D+
(2) +d+=+120%2A2.8+
(2) +d+=+336+
The distance between the two airports
is 336 mi