SOLUTION: A 555-mile, 5 hour plane trip was flown at two speeds. For the first par of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was

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Question 1067795: A 555-mile, 5 hour plane trip was flown at two speeds. For the first par of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs spent driving at 105 mi/hr
+5+-+t+ = time in hrs spent driving at 115 mi/hr
Let +d+ = distance in miles driven at 105 mi/hr
+555+-+d+ = distance in miles driven at 115 mi/hr
------------------------------------------------
For 105 mi/hr part of trip:
(1) +d+=+105t+
For 115 mi/hr part of trip:
(2) +555+-+d+=+115%2A%28+5+-+t+%29+
-------------------------------
(2) +555+-+d+=+575+-+115t+
(2) +d+=+115t+-+20+
Substitute (1) into (2)
(2) +105t+=+115t+-+20+
(2) +10t+-+20+
(2) +t+=+2+
and
+5+-+t+=+5+-+2+
+5+-+t+=+3+
---------------------
2 hrs = time spent driving at 105 mi/hr
3 hrs = time spent driving at 115 mi/hr
---------------------------------------
check:
(1) +d+=+105t+
(1) +d+=+105%2A2+
(1) +d+=+210+ mi
and
(2) +555+-+d+=+115%2A%28+5+-+t+%29+
(2) +555+-+d+=+115%2A%28+5+-+2+%29+
(2) +555+-+d+=+115%2A3+
(2) +555+-+d+=+345+
and
+210+%2B+345+=+555+
OK