PSAT Math Multiple-Choice Question 209: Answer and Explanation

Question: 209

From	Distance to LHR
DCA	3,718
MIA	4,470

Two airplanes departed from different airports at 5:30 a.m., both traveling nonstop to London Heathrow Airport (LHR). The distances the planes traveled are recorded in the table. The Washington, D.C. (DCA) flight flew through moderate cloud cover and as a result only averaged 338 miles per hour. The flight from Miami (MIA) had good weather conditions for the first two-thirds of the trip and averaged 596 miles per hour, but then encountered some turbulence and only averaged 447 miles per hour for the last part of the trip. Which plane arrived first and how long was it at the London airport before the other plane arrived?

• A. MIA; 2 hours, 40 minutes
• B. MIA; 3 hours, 30 minutes
• C. DCA; 1 hour, 20 minutes
• D. DCA; 3 hours, 40 minutes

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Problem Solving and Data Analysis/Rates, Ratios, Proportions, and Percents

Getting to the Answer: Questions that involve distance, rate, and time can almost always be solved using the formula Distance = rate × time. Break the question into short steps (first part of trip, second part of trip). Start with the plane from DCA. Use the speed, or rate, of the plane, 338 miles per hour, and its distance from London, 3,718 miles, to determine when it arrived. You don't know the time, so call it t:

It took the DCA flight 11 hours. Now, determine how long it took the plane from MIA. You'll need to find the distance for each part of the trip—the question only tells you the total distance. Then, use the formula to find how long the plane flew at 596 miles per hour and how long it flew at 447 miles per hour.

First Part of Trip	Second Part of Trip

This means it took the MIA flight 5 hours + 3 hours, 20 minutes = 8 hours, 20 minutes. So, the plane from MIA arrived first. It arrived 11 hours - 8 hours, 20 minutes = 2 hours, 40 minutes before the plane from DCA, so (A) is correct.