PSAT Math Multiple-Choice Question 47: Answer and Explanation

Question: 47

Maggie and Glenn both leave from the same house to go for a jog along a trail. Shortly after leaving, Maggie realizes she forgot her iPhone and returns home to find it before heading back out onto the same trail. The graph above shows how far each of them is from home for the first fifteen minutes of their jogs. Excluding the time she spends at home, which of the following is closest to Maggie's average speed, in meters per second, during the portion of her jog shown?

• A. 2.3
• B. 5
• C. 6.3
• D. 140

Correct Answer: C

Explanation:

C

The question asks for a rate in terms of meters per second, so use the rate formula D = RT, in which D is the distance, R is the rate or speed, and T is the time. First, calculate the total distance that Maggie runs. She runs 1,200 meters before turning around and running another 1,200 meters to return home. She then runs 2,100 more meters after retrieving her iPhone. Therefore, she runs a total of 4,500 meters (1,200 + 1,200 + 2,100). Next, find the total time that Maggie ran. Because she was at home for 3 minutes, the total time she spent running out of the 15 minutes shown on the graph was 12 minutes (15 - 3). The question asks for speed in meters per second, so convert the 12 minutes to seconds by multiplying 12 × 60 = 720. Fill in the rate formula with the distance of 4,500 meters and time of 720 seconds to get 4,500 = R(720). To find the average speed or R, divide the total both sides by 720 to get 6.3 = R. The correct answer is (C).