Question

George walks $1$ mile to school. He leaves home at the same time each day, walks at a steady speed of $3$ miles per hour, and arrives just as school begins.

Today he was distracted by the pleasant weather and walked the first $\frac{1}{2}$ mile at a speed of only $2$ miles per hour. At how many miles per hour must George run the last $\frac{1}{2}$ mile in order to arrive just as school begins today?

$4$

$6$

$8$

$10$

$12$

Solution:

If George normally walks $1$ mile at $3$ miles per hour, it takes him $\dfrac{1}{3}$ hour, or $20$ minutes, to get to school.

Today he walked the first $\dfrac{1}{2}$ mile at $2$ miles per hour, taking $\dfrac{1}{2}\div2=\dfrac{1}{4}$ hour, or $15$ minutes. He has $5$ minutes, which is $\dfrac{1}{12}$ hour, left to cover $\dfrac{1}{2}$ mile.

His required speed is $\dfrac{1}{2}\div\dfrac{1}{12}=6$ miles per hour.

Thus, B is the correct answer.

2014 AMC 8 Problem 17

Solution:

Problem 17 in Other Years