2010 AMC 12B Problem 7

Below is the professionally curated solution for Problem 7 of the 2010 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 12B solutions, or check the answer key.

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Concepts:distance rate and time linear equation

Difficulty rating: 1240

Shelby drives her scooter at a speed of $30$ miles per hour if it is not raining, and $20$ miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of $16$ miles in $40$ minutes. How many minutes did she drive in the rain?

$18$

$21$

$24$

$27$

$30$

Solution:

Let $t$ be the number of minutes driven in the rain. She covers $20\cdot\frac{t}{60}$ miles in the rain and $30\cdot\frac{40-t}{60}$ miles in the sun.

Setting the total to $16$ gives $\frac{20t+30(40-t)}{60}=16,$ so $1200-10t=960$ and $t=24.$

Thus, the correct answer is C.

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