PSAT Math Multiple-Choice Question 671: Answer and Explanation

Question: 671

A car and a truck are initially 180 miles apart and are driving toward each other on a straight road when an observer measures their respective speeds. The car is driving at a constant speed of x miles per hour, and the truck is going twice this speed. If the car and the truck meet each other after three hours of driving, what is the speed of the truck?

• A. 20 mph
• B. 30 mph
• C. 40 mph
• D. 60 mph

Correct Answer: C

Explanation:

(C) We will use the formula d = rt, where d is distance, r is rate, and t is time. Let's define the car's initial position, s, as s = 0 and the truck's initial position as s = 180.

The car's position at time t will be its initial position (0) plus the distance it has traveled in that time. We are told that the car's rate r is x, so the distance the car travels in time t is xt. Since the car starts at an initial position of 0, its position at time t will be expressed as s = xt + 0 = xt.

The truck starts at position s =180 and travels toward the 0 position. So the truck's position at time t will be expressed as 180 minus the distance it has traveled in time t. Its speed is twice the speed of the car, or 2x. So the truck's position at time t will be expressed as s = 180 - 2xt.

They meet where their positions are equal. So set the two equations equal to one another to solve for x:

xt = 180 - 2xt

We know that the vehicles meet after 3 hours, so we can plug in 3 for t:

3x = 180 - 6x

Adding 6x to both sides gives:

9x = 180

Dividing both sides by 9 tells results in x = 20.

However, before selecting choice (A), make sure to finish the problem.

The question asks you what speed the truck is going. The truck has a speed of 2x. So its speed is 2(20) = 40, which is choice (C).