06/03/2020 (2019: AMC 8, Problem 16)

Q: Qiang drives 15 miles at an average speed of 30 miles per hour. How many additional miles will he have to drive at 55 miles per hour to average 50 miles per hour for the entire trip?

Because Qiang drove at 15 miles at 30 mph, that means he drove for 15/30 = .5 hours. We set up an equation, where the numerator is miles traveled, and the denominator is the time: 50 = (15 + 55x)/(.5 + x), where x is the number of hours he'll have to drive for.

We multiply both sides by (.5 + x) and get: 25 + 50x = 15 + 55x.

We isolate the variable and get: 25 - 15 = 55x - 50x, which simplifies to 10 = 5x, which simplifies to 2 = x. That means he has to drive for 2 more hours.

2 hours * 55 mph = 110 miles, so the answer is D.