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by DFritschy » Tue Aug 28, 2012 3:36 pm
Sarah drove an average speed of 30 miles per hour for the first 30 miles of her trip. She drove an average of 60 miles per hour the remaining 30 miles of her trip. What was the average speed of her entire trip?

A) 33 mph B) 40 mph c) 50 mph D) 52 mph E) 55 mph
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by SmartAssJun » Tue Aug 28, 2012 4:46 pm
DFritschy wrote:Sarah drove an average speed of 30 miles per hour for the first 30 miles of her trip. She drove an average of 60 miles per hour the remaining 30 miles of her trip. What was the average speed of her entire trip?

A) 33 mph B) 40 mph c) 50 mph D) 52 mph E) 55 mph
It took her 1 hour for the first 30 (30/30) mile trip and then 1/2(30/60) hours for the rest.
So the total 60 mile trip took her 3/2 hours. The average speed then should be 40(60*2/3) miles per hour.
So B
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by Ian Stewart » Tue Aug 28, 2012 5:32 pm
I have nothing to add to the solution above, which is perfect, but with those answer choices, you don't actually need to do any work if you understand weighted averages reasonably well.

Average speed is a weighted average, weighted by the time spent at each speed. If you drive equal distances at 30 and at 60 miles per hour, you'll spend longer driving at 30 miles per hour. So the answer needs to be closer to 30 than to 60. Only A and B are possible, and A is way too small, so B needs to be right.
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by js0704 » Wed Aug 29, 2012 12:54 pm
I just went:

30 mi in 1 hr
30 mi in 0.5 hr

60 mi in 1.5 hr = 60/1.5 = 40 mph
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