Distance Formulas: Calculations & Examples

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• 0:03 Solve for Distance
• 2:12 Solve for Rate
• 3:01 Solve for Time
• 3:45 Distance Plus Distance
• 4:39 Distance and Fuel
• 5:52 Lesson Summary

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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Let's go on a road trip! In this lesson, we'll practice calculations involving distance, rate and time. We'll also look at how we determine the relationship between distance and fuel.

Solve for Distance

How fast can you run? How far does your car go on a tank of gas? If you keep going on your bike at a constant speed, how long will it take to get to the next town?

These are the problems that vex us. Well, OK, these are problems that vex me, particularly on long drives in big, open states like Wyoming, where I really want to know how quickly I can get from point A to point B.

Fortunately, there are formulas we can use to solve problems like these. What's better is that they're simple enough that you might even be able to do them in your head while speeding along the interstate and eating french fries, though hopefully not also using your phone. That's totally dangerous.

Let's start with the distance formula. The standard distance formula, which is also known as the uniform rate formula, is d = rt. D stands for distance, r for rate and t for time.

How can we use this? Well, what if we know the speed of something and how long it's moving, but not how far it goes? Here's a sample problem:

Sarah runs at an average rate of 7.5 miles per hour for 2 hours. How far does she go?

Let's start by identifying what we know from our formula. Our r, or rate, is 7.5 miles per hour. Our t, or time, is 2 hours. So d = 7.5 * 2. Note that we're multiplying miles per hour times hours. If we were to write this properly, it would be 7.5miles/1 hour * 2 hours. The hours cancel out, leaving us with just miles.

Since we're trying to find distance, it makes sense that our answer will be in miles. But always be sure that you're using the same language. If you're given time in minutes, make sure your rate is in minutes. If not, you'll need to convert one or the other. If you're given miles per hour and the question asks about kilometers or parsecs or something like that, well, then your conversion might get a little messy.

But here we just want to know how many miles Sarah goes. Again, we have d = 7.5 * 2. That means d = 15. So Sarah ran 15 miles. That's awesome!

Solve for Rate

The distance formula is nicely versatile. It's not all about how far Sarah can run, though that's very impressive. We can rewrite the distance formula if, instead of distance, we're solving for something else, like the rate. Here's a rate problem:

A train travels 438 miles in 6 hours. What is its average speed?

Let's look at our distance formula: d = rt. Here we know our d is 438 and our t is 6. We want to know r. So we can rewrite the formula as r = d/t. All we did is divide by t to move the t over.

So r = 438/6. And that's 73. So, this train traveled at an average speed of 73 mph. That's a pretty fast train.

Solve for Time

That's solving for r; what about solving for t? That brings us to distance formula iteration #3: t = d/r. Here's a problem where this is useful:

Mike walks at a rate of 3 miles per hour. If he needs to walk 26.2 miles, how long will his trip last?

So Mike's walking a marathon. Why? I don't know. That's between Mike and his soon-to-be-tired feet. But we can figure this out. If t = d/r, then we have t = 26.2/3. That's 8.73. .73 is about 44 minutes. So, Mike will be walking for 8 hours and 44 minutes. That's a long walk.

Distance Plus Distance

With this next one, we're going to try something different: distance plus distance. Here's the problem:

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