2007 AMC 12A Problem 4

Below is the professionally curated solution for Problem 4 of the 2007 AMC 12A, 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.

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Concepts:distance rate and time

Difficulty rating: 1130

Kate rode her bicycle for $30$ minutes at a speed of $16$ mph, then walked for $90$ minutes at a speed of $4$ mph. What was her overall average speed in miles per hour?

$7$

$9$

$10$

$12$

$14$

Solution:

Kate rode for $\tfrac12$ hour at $16$ mph, covering $8$ miles.

She walked for $\tfrac32$ hours at $4$ mph, covering $6$ miles.

She covered $14$ miles in $2$ hours, so her average speed was $7$ mph.

Thus, the correct answer is A.

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