2014 AMC 12A Problem 11

Problem 11 of 25IntermediateAlgebra

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?

Show solution

Solution

Let

d

be the remaining distance after one hour and

t

the remaining time until the flight. At

35

mph he would be an hour late, so

d=35(t+1).

50

mph he is half an hour early, so

d=50\left(t-\tfrac12\right).

Setting these equal gives

35t+35=50t-25,

t=4

and

d=175.

The total distance is

175+35=210

miles. Thus, the correct answer is C.