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?

$2.0$

$2.2$

$2.8$

$3.4$

$4.4$

Solution:

Let the distance she walked be $d.$ Since this is the same as the amount she biked, represented as $s,$ we know that $d=s.$

Furthermore, let the time she walked (in hours) be $t.$ Therefore, the amount of time she biked is $\dfrac{44}{60}-t.$

Now, using the definition of speed, we can see that $5 = \frac st$ $17 = \dfrac s{\frac{44}{60}-t}$ This implies that: $s=5t = 17\left(\frac{44}{60}-t\right)$ so $22t = \frac{17\cdot 44}{60}$ Therefore, $t = \frac{17}{30}$ Since $s=5t,$ we have $s = 5\cdot \frac{17}{30} = \frac{17}{6}$ which approximates to $2.8.$

Thus, the correct answer is C .

2017 AMC 10B Problem 7

Solution:

Problem 7 in Other Years