Step-by-step explanation:
Distance word problems are a common type of algebra word problems. They involve a scenario in which you need to figure out how fast, how far, or how long one or more objects have traveled. These are often called train problems because one of the most famous types of distance problems involves finding out when two trains heading toward each other cross paths.
In this lesson, you'll learn how to solve train problems and a few other common types of distance problems. But first, let's look at some basic principles that apply to any distance problem.
The basics of distance problems
There are three basic aspects to movement and travel: distance, rate, and time. To understand the difference among these, think about the last time you drove somewhere.
The distance is how far you traveled. The rate is how fast you traveled. The time is how long the trip took.
The relationship among these things can be described by this formula:
distance = rate x time
d = rt
In other words, the distance you drove is equal to the rate at which you drove times the amount of time you drove. For an example of how this would work in real life, just imagine your last trip was like this:
You drove 25 miles—that's the distance.
You drove an average of 50 mph—that's the rate.
The drive took you 30 minutes, or 0.5 hours—that's the time.
According to the formula, if we multiply the rate and time, the product should be our distance.
And it is! We drove 50 mph for 0.5 hours—and 50 ⋅ 0.5 equals 25, which is our distance.
What if we drove 60 mph instead of 50? How far could we drive in 30 minutes? We could use the same formula to figure this out.
60 ⋅ 0.5 is 30, so our distance would be 30 miles.
Solving distance problems
When you solve any distance problem, you'll have to do what we just did—use the formula to find distance, rate, or time. Let's try another simple problem.
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