PSAT Math Multiple-Choice Question 49: Answer and Explanation

Question: 49

The college that Everett attends in Chicago is exactly 200 miles from his parents' home. When his parents come to visit him at school, they drive at an average speed of 45 miles per hour for maximum safety. When Everett drives home for winter break, his average speed is x% greater than the average speed at which his parents drive when they make the trip. Which of the following represents the time Everett saves on the 200-mile trip compared with his parents' average time, in hours?

• A.
• B.
• C.
• D.

Correct Answer: C

Explanation:

C

The question asks for the difference in the amount of time a certain trip takes at two different speeds. The question also asks about rates, 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 time it takes Everett's parents to make the trip. Fill in the formula with the distance of 200 miles and the parents' rate of 45 miles per hour to get 200 = (45)T. To find the time the trip takes Everett's parents in hours, divide both sides by 45 to get 4.4 hours = T. Next, find the time it takes Everett to make the trip. There is a variable in the problem and in the answer choices, so plug in. Because the question is dealing with percentages, make x = 100. If Everett is driving at a speed 100% greater than his parents' speed, then he is driving at 90 mph. Fill this information into the rate formula to find Everett's time. The formula becomes 200 = (90)T, so the time for Everett's trip is T = 2.2 hours. The difference in the amount of time the trip takes for Everett versus his parents is 4.4 - 2.2 = 2.2. This is the target value; circle it. Now plug x = 100 into the answer choices to see which one matches the target value. Choice (A) becomes . Continue simplifying to get = -2.2. Choice (A) is a negative value, which does not match the target, so eliminate (A). Choice (B) becomes . This becomes , and because the denominator is 0, (B) is undefined. Eliminate (B). Choice (C) becomes . Continue simplifying to get = 2.2. This matches the target, so keep (C), but check (D) just in case. Choice (D) becomes . Continue simplifying to get = 0.1125. Eliminate (D). The correct answer is (C).