Cool AMC 10 problem

Level 2

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?

The answer is 210.

1 solution

Khang Nguyen Thanh
Jul 4, 2016

Note that he drives at $50$ miles per hour after the first hour and continues doing so until he arrives.

Let $d$ be the distance still needed to travel after the first $1$ hour.

We have that $\dfrac{d}{50}+1.5=\dfrac{d}{35}$ , where the $1.5$ comes from $1$ hour late decreased to $0.5$ hours early.

Simplifying gives $7d+525=10d$ , or $d=175$ .

Now, we must add an extra $35$ miles traveled in the first hour, giving a total of $\boxed{210}$ miles.

Cool AMC 10 problem

The answer is 210.

1 solution

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