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Word Problems Involving Time, Distance & Velocity

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  • 0:02 Time, Distance &…
  • 1:22 Solving for Velocity
  • 4:14 Solving for Time
  • 5:50 Solving for Distance
  • 7:32 Lesson Summary
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Lesson Transcript
Instructor: Julie Zundel

Julie has taught high school Zoology, Biology, Physical Science and Chem Tech. She has a Bachelor of Science in Biology and a Master of Education.

Knowing how long something takes, how far away something is, and how fast you need to travel, are all important factors in your day. This lesson will give you the tools to calculate time, distance, and velocity in word problems.

Time, Distance, and Velocity Defined

Your flight to Hawaii leaves in an hour, and the airport is 30 miles away. How fast do you need to drive in order to catch your flight? A problem like this may sound scary, but this lesson will teach you everything you need to know in order to successfully catch your flight and complete word problems involving time, distance, and velocity.

Time, of course, refers to how long something takes and can be measured in a variety of units, such as minutes, hours, and even days. Distance measures the space between two places (in this case, you and the airport) and can be measured in units such as centimeters, meters, inches, and miles. Finally, velocity is speed with direction, and can be measured in units such as inches per minute or miles per hour. Before we go on, take a look at the table on your screen so you can familiarize yourself with some examples of units associated with distance, time, and velocity.

Distance Time Velocity
centimeter millisecond centimeters per millisecond
meter second meters per second
inches minute inches per minute
mile minute miles per minute
mile hour miles per hour

As you can see a the smallest level, for example, a centimeter is a measurement of distance, a millisecond is a measurement of time, and centimeters per millisecond is a measurement of velocity. You can see this with all the other measurements in this table, whether it's meters per second or miles per hour. Now that you know what each term means, let's do some word problems!

Solving for Velocity

Let's go back to our Hawaii problem. You don't want to miss the flight, so we'd better figure out how fast you need to go. Specifically, we'll look at the average velocity, or the displacement divided by the time. Displacement is how far you've traveled from a starting point.

The airport is 30 miles south and you have one hour to get there, so how fast do you need to travel? Remember, velocity is speed and direction, so let's pretend the road to the airport doesn't bend or wind. Start the problem by determining the variables, or letters that represent velocity, time, and distance. Let's use t for time, d for distance, and v for velocity.

You know that distance can be measured in miles, so 30 miles must be the distance, and that time can be measured in hours, so 1 hour must be the time. We're trying to figure out the velocity. Set it up to look something like this:

  • d = 30 miles
  • t = 1 hour
  • v = ?

Now I am going to show you a little trick to solve all of these problems. Take a look at this diagram on screen for the formula.

Image A
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In order to determine the formula, you need to cover up the variable you are looking for (in this case, v or velocity). You can now see we covered up the v with a circle.

Image B
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Build your formula reading from top to bottom, in this case. The formula you are going to use here is: v = d / t. Plug in each variable into the formula and you get:

v = 30 miles / 1 hour

Perform the calculation and you get:

v = 30 miles per hour

If you want to be napping on the beach, you need to drive at least 30 miles per hour to catch your flight! This problem seemed pretty straightforward and you're probably thinking there isn't any difference between speed and velocity, right?

Let's make this problem a little more challenging. Let's say the road to the airport was 20 miles east and then 10 miles west, and you couldn't have a straight shot because of a mountain. Remember, velocity looks at speed and direction, so this will change things a little.

So to calculate the average velocity, we will need look at the displacement. Here you need to look at how far you actually traveled from your starting point. Start by assigning variables like before:

  • t = 1 hour
  • v = ?

Distance is no longer 30 miles. It's 20 miles - 10 miles because we are looking at displacement.

  • d = 10 miles

Now you can solve like before:

v = 10 miles per hour

You can see how the direction you are going changes your answer, right? Now this would be a little confusing if you were trying to get to the airport on time, but it's important to see how direction affects your answers for velocity.

Solving for Time

Now that you know how to solve for velocity, let's do a problem where we solve for time, or t.

While in Hawaii, you planned several activities, but you're afraid you're going to be late for scuba diving since you've gotten held up on your horseback riding adventure. You need to figure out how much longer you will be horseback riding to see if you can make it before your scuba diving boat departs. You have to go three miles west to get back to your car, and your horse is traveling five miles per hour. How much longer until you reach your car?

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