ASVAB Study Guide
Word Problems · Lesson 1 of 8

Distance, Rate, and Time (D = RT)

Key rules and formulas, worked examples and 6 practice problems with step-by-step solutions.

1.Basic Motion

Relationship between distance, speed, and time.

$$D = R \times T$$

D: Distancer

R: Rate (Speed)

T: Time

Example

A car travels at 60 mph for 30 munutes. What is the distance?

Show solution

Step 1: Use $$D= R \times T$$

Step 2: $$T = \frac{30}{60} = 0.5$$ hour

Step 3: $$D= 60 \times 0.5 = 30$$ miles

Practice problems

  1. Problem 1

    A motorist drives a distance of 45 miles at a constant speed of 60mph. How many minutes does the trip take?

    Show solution

    Answer: $$T= 45$$ minutes

    Step 1: Use $$T = \frac{D}{R}$$

    Step 2: $$T = \frac{45}{60} = 0.75$$ hour

    Step 3: Convert $$T= 0.75 \times 60 = 45$$ minutes

  2. Problem 2

    An athlete runs a 10 miles race and finishes it in exactly 1.25 hours. What was the runner's average speed in miles per hour (mph)?

    Show solution

    Answer: $$R = 8$$ mph

    Step 1: Use $$R = \frac{D}{T}$$

    Step 2: Identify $$D = 10$$ miles, $$T = 1.25$$ hours

    Step 3: Calculate $$R = \frac{10}{1.25} = 8$$ mph

  3. Problem 3

    A motorcycle travels at a constant speed of 50 mph for 90 minutes. What is the distance?

    Show solution

    Answer: $$D = 75$$ miles

    Step 1: Use $$D = R \times T$$

    Step 2: Convert $$T = \frac{90}{60} = 1.5$$ hours

    Step 3: Calculate $$D = 50 \times 1.5 = 75$$ miles

Remember

Speed and time must be in the same unit. If speed is measured in mph, then time must also be measured in hours.

2.Opposite Directions

Two objects moving away from or toward each other.

$$D = (R_1 + R_2) \times T$$

Add the rates because the distance between them changes by their combined speed.

Example

Two cars start from the same town and travel in opposite directions. One car travels at 50 mph, and the other travels at 60 mph. How far apart are they after 30 minutes?

Show solution

Step 1: Use $$D = (R_1 + R_2) \times T$$

Step 2: $$T = \frac{30}{60} = 0.5$$ hour

Step 3: $$D = (50 + 60) \times 0.5 = 55$$ miles

Practice problems

  1. Problem 4

    Two pedestrians start at the same point and walk in opposite directions. One walks at 3 mph, and the other walks at 4 mph. How far apart are they after 45 minutes?

    Show solution

    Answer: $$D = 5.25$$ miles

    Step 1: Use $$D = (R_1 + R_2) \times T$$

    Step 2: Convert $$T = \frac{45}{60} = 0.75$$ hour

    Step 3: Calculate $$D = (3 + 4) \times 0.75 = 5.25$$ miles

  2. Problem 5

    A motorist drives east at 45 mph and a cyclist rides west at 15 mph from the same point. How many minutes does it take for them to be 30 miles apart?

    Show solution

    Answer: $$T = 30$$ minutes

    Step 1: Use $$T = \frac{D}{(R_1 + R_2)}$$

    Step 2: $$T = \frac{30}{(45 + 15)} = 0.5$$ hour

    Step 3: Convert $$T = 0.5 \times 60 = 30$$ minutes

  3. Problem 6

    Two planes start from the same airport and fly in opposite directions. After 30 minutes, they are 250 miles apart. If Plane X flies at 240 mph, what is the speed of Plane Y

    Show solution

    Answer: $$R_2 = 260$$ mph

    Step 1: Convert $$T = \frac{30}{60} = 0.5$$ hour. Use Combined Rate = D / T

    Step 2: Calculate Combined Rate $$= \frac{250}{0.5} = 500$$ mph

    Step 3: Find $$R_2 = 500 - 240 = 260$$ mph