SOLUTION: You drive from Fox to Nenana(60 miles) at 30 mph. At what rate would you have to drive back to fox so that the average rate for the entire trip is 60 mph.

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Question 947363: You drive from Fox to Nenana(60 miles) at 30 mph. At what rate would you have to drive back to fox so that the average rate for the entire trip is 60 mph.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Average rate is always ( total distance ) / ( total time )
The total distance is:
+60+%2B+60+=+120+ mi
---------------------
Time for Fox - Nenana trip:
+t+=+d%2Fr+
+t+=+60%2F30+
+t+=+2+ hrs
---------------
Time for Nenana - Fox trip:
Let +r+ = the rate for this trip
+t+=+60%2Fr+
----------------
The total time is:
+2+%2B+60%2Fr+
-----------------
Average for the whole trip =
+60+ mi/hr
+60+ = ( total distance ) / ( total time )
+60+=+120+%2F+%28+2+%2B+60%2Fr+%29+
Multiply both sides by +2+%2B+60%2Fr+
+60%2A%28+2+%2B+60%2Fr+%29+=+120+
+2+%2B+60%2Fr+=+2+
+60%2Fr+=+0+
+r+ = infinity!
There is no way you can average +60+ mi/hr
with the data given
----------------------
Suppose your speed for Fox - Nenana was
+31+ mi/hr instead of +30+ mi/hr
+t+=+60%2F31+
+t+=+1.9355+ hrs
-------------------
Then you end up with:
+60+=+120%2F%28+1.9355+%2B+60%2Fr+%29+
+60%2A%28+1.9355+%2B+60%2Fr+%29+=+120+
+1.9355+%2B+60%2Fr+=+2+
+60%2Fr+=+.0645+
+r+=+60%2F.0645+
+r+=+930.233+
Now your speed doesn't have to be infinite,
but it is still impossible
You have to make the trip back at
something like +60+ mi/hr