2017 AMC 12B Problem 4

Question

Samia set off on her bicycle to visit her friend, traveling at an average speed of

17

kilometers per hour. When she had gone half the distance to her friend’s house, a tire went flat, and she walked the rest of the way at

5

kilometers per hour. In all it took her

44

minutes to reach her friend’s house. In kilometers rounded to the nearest tenth, how far did Samia walk?

2.0

2.2

2.8

3.4

4.4

Let

d

be the one-way distance she biked (and also walked); use time

= \dfrac{\text{distance}}{\text{rate}}

Solve

\dfrac{d}{17} + \dfrac{d}{5} = \dfrac{44}{60}

for

d

Let

2d

be the total distance, so she biked

d

at

17

km/h and walked

d

at

5

km/h. The total time in hours is

\frac{d}{17} + \frac{d}{5} = \frac{44}{60}.

Combining the left side gives

\dfrac{22d}{85} = \dfrac{11}{15},

so

d = \dfrac{11}{15} \cdot \dfrac{85}{22} = \dfrac{17}{6} = 2.833\ldots

She walked about

2.8

kilometers.

Thus, the correct answer is C.

Problem 4 in other years