SOLUTION: You are to travel from point A to point B and return.On the trip from A to B,you travel at 30 miles per hour. How fast would you have to travel from B to A in order to average 60 m

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Question 544531: You are to travel from point A to point B and return.On the trip from A to B,you travel at 30 miles per hour. How fast would you have to travel from B to A in order to average 60 miles per hour fro the round trip?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Average speed is always ( total distance ) / ( total time )
Call the distance between A and B d
Let r = rate on B to A trip
Going from A to B:
+d+=+30t%5B1%5D+
+t%5B1%5D+=+d%2F30+
Going from B to A:
+d+=+r%2At%5B2%5D+
+t%5B2%5D+=+d%2Fr+
The average speed is
+%282d%29+%2F+%28+t%5B1%5D+%2B+t%5B2%5D+%29+
+%282d%29+%2F+%28d%2F30+%2B+d%2Fr+%29+
Divide top and bottom by d
+2+%2F+%28+1%2F30+%2B+1%2Fr+%29+
If average speed is 60 mi/hr,
+60+=+2+%2F+%28+1%2F30+%2B+1%2Fr+%29+
+60%2A%28+1%2F30+%2B+1%2Fr+%29+=+2+
+2+%2B+60%2Fr+=+2+
+60%2Fr+=+0+
+r+ has to be infinite, so you can't possibly average 60 mi/hr
check: What if average speed must be 59 mi/hr?
+59+=+2+%2F+%28+1%2F30+%2B+1%2Fr+%29+
+59%2A%281%2F30+%2B+1%2Fr+%29+=+2+
+59%2F30+%2B+59%2Fr+=+2+
+59%2Fr+=+60%2F30+-+59%2F30+
+59%2Fr+=+1%2F30+
Multiply both sides by 30r
+59%2A30+=+r+
++r+=+1770+ mi/hr
This is OK for a rocket to space, but not a vehicle.
The average speed needs to be lower still