2007 AMC 12A Problem 4

Attempt Problem 4 of the 2007 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

4.

Kate rode her bicycle for 3030 minutes at a speed of 1616 mph, then walked for 9090 minutes at a speed of 44 mph. What was her overall average speed in miles per hour?
77
99
1010
1212
1414
Answer: A
Concepts:distance rate and time
Small hint:
Average speed is total distance divided by total time, not the average of the two speeds
Big hint:
She rides 88 miles and walks 66 miles over a total of 22 hours
Solution:
Kate rode for 12\tfrac12 hour at 1616 mph, covering 88 miles.
She walked for 32\tfrac32 hours at 44 mph, covering 66 miles.
She covered 1414 miles in 22 hours, so her average speed was 77 mph.
Thus, the correct answer is A.
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