2010 AMC 12B Problem 7

Question

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

Let

t

be the minutes in the rain; convert each speed to miles per minute

Rain distance

20\cdot\dfrac{t}{60}

plus sun distance

30\cdot\dfrac{40-t}{60}

equals

16

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.

Problem 7 in other years