Question

David drives from his home to the airport to catch a flight. He drives $35$ miles in the first hour, but realizes that he will be $1$ hour late if he continues at this speed. He increases his speed by $15$ miles per hour for the rest of the way to the airport and arrives $30$ minutes early. How many miles is the airport from his home?

$140$

$175$

$210$

$245$

$280$

Solution:

Note that David drives at $50$ miles per hour after one hour. Let the distance he still needs to be drive be $d.$

Then, if the airport is $x$ miles from David's house, we know that: $\dfrac x{35} - \left(1+\dfrac{x-35}{50}\right) = \dfrac 32$ We solve this equation as follows: $\begin{align*} \dfrac x{35} - \left(1+\dfrac{x-35}{50}\right) &= \dfrac 32\\ \dfrac x{35} - \dfrac{x-35+50}{50} &= \dfrac 32\\ 10x - 7(x+15)&= 525\\ 10x - 7x-105&= 525\\ 3x&= 630\\ x&=210 \end{align*}$ Therefore, the airport is $x=210$ miles from David's house.

Thus, C is the correct answer.

2014 AMC 10A Problem 15

Solution:

Problem 15 in Other Years