SOLUTION: Both planes were headed from the Outer Boondocks to Timbuktu. Plane #1 traveled at 450 mph and plane #2 at 500 mph. If plane #1 took off 1 hour before plane #2, how many hours di

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Both planes were headed from the Outer Boondocks to Timbuktu. Plane #1 traveled at 450 mph and plane #2 at 500 mph. If plane #1 took off 1 hour before plane #2, how many hours di      Log On

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Question 1156786: Both planes were headed from the Outer Boondocks to Timbuktu. Plane #1 traveled at 450 mph and plane #2 at 500 mph. If plane #1 took off 1 hour before plane #2, how many hours did it take for plane #2 to catch plane #1?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plane 1's head start is:
+d%5B1%5D+=+450%2A1+
+d%5B1%5D+=+450+ mi
Start a stopwatch when plane 2 takes off
Let +t+ = time on stopwatch when
plane 2 catches plane 1
Let +d+ = plane 2 travels until it catches
plane 1
----------------------------
Plane 1 equation:
(1) +d+-+450+=+450t+
Plane 2 equation:
(2) +d+=+500t+
----------------------------
Plug (2) into (1)
(1) +500t+-+450+=+450t+
(1) +50t+=+450+
(1) +t+=+9+
It takes plane 2 9 hrs to catch plane 1
-------------------------
check:
(2) +d+=+500t+
(2) +d+=+500%2A9+
(2) +d+=+4500+
and
(1) +d+-+450+=+450t+
(1) +d+-+450+=+450%2A9+
(1) +d+=+450%2A10+
(1) +d+=+4500+
OK