2017 AMC 10B Problem 7

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 the walking distance be

d

, so the biking distance is also

d

Add the biking time and walking time to get

44

minutes

Let

d

be the distance Samia walked. She bicycled the same distance, so her total travel time gives

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

Solving yields

d=\dfrac{17}{6}=2.833\ldots,

which rounds to

2.8

kilometers.

Thus, the correct answer is C .

Problem 7 in other years