SOLUTION: A motorist travels 120 miles from Antwerp to Brussels at an average of 40 mph. She returns over the same road at X mph. Her average rate for the whole trip is 48 mph. What is the v

Question 759862: A motorist travels 120 miles from Antwerp to Brussels at an average of 40 mph. She returns over the same road at X mph. Her average rate for the whole trip is 48 mph. What is the value of X?
I have been working on this problem for a while and I have no idea how to solve it. Help is dearly apreciated! :)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A motorist travels 120 miles from Antwerp to Brussels at an average of 40 mph. She returns over the same road at X mph. Her average rate for the whole trip is 48 mph. What is the value of X?
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120 miles at 40 mi/hr takes 3 hours.
The round trip is 240 miles, at 48 mi/hr avg --> 5 hours total.
--> 2 hours for the return
120 mi/2 hr = 60 mi/hr
x = 60 mi/hr
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Notice that a round-trip at 40 & 60 is not the average of 40 & 60.
The average is always less than the average of 2 unequal speeds.
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Avg for RT = 2*r1*r2/(r1 + r2)
For 60 & 40,
Avg - 2*60*40/(60+40) = 48 mi/hr

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