2010 AMC 10B Problem 10

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 rain time in minutes

Use

20\cdot\dfrac{t}{60}+30\cdot\dfrac{40-t}{60}=16

Note that

40

minutes is

\frac{2}{3}

hours. Let Shelby drive

h

hours in the sun.

Then she drives

\frac{2}{3} - h

hours in the rain, which means she travels a total of

30h + 20\left(\dfrac{2}{3} - h\right) = 10h + \dfrac{40}{3}

miles. We have this equals

16,

so

10h + \dfrac{40}{3} = 16

h = \dfrac{4}{15}.

Then Shelby drives

60\left(\dfrac{2}{3} - \dfrac{4}{15}\right) = 60 \cdot \dfrac{2}{5} = 24

minutes in the rain.

Thus, C is the correct answer.

Problem 10 in other years