3/9/2023 0 Comments 120 number fill in free![]() Since we're solving for r, we'll have to get it alone on one side of the equation. The rate is represented by r because we don't yet know how fast Janae was walking. Next, we'll fill in the formula with the information from our table. ![]() Janae walked one-and-a-half miles or 1.5 miles in a half hour, or 0.5 hours.Īs always, we start with our formula. The table is repeating the facts we already know from the problem. We can picture Janae's walk as something like this:Īnd we can set up the information from the problem we know like this: distance What was her average speed in miles per hour? For example, take a look at this problem:Īfter work, Janae walked in her neighborhood for a half hour. In the problem we just solved we calculated for distance, but you can use the d = rt formula to solve for rate and time too. However, what if the time had been written in a different unit, like in minutes? In that case, you'd have to convert the time into hours so it would use the same unit as the rate. It's possible to multiply 65 miles per hour by 2.5 hours because they use the same unit: an hour. In other words, the distance Lee drove from his house to the zoo is 162.5 miles.īe careful to use the same units of measurement for rate and time. We have an answer to our problem: d = 162.5. To find d, all we have to do is multiply 65 and 2.5. The unknown distance is represented with the variable d. The formula d = rt looks like this when we plug in the numbers from the problem. We can use the distance = rate ⋅ time formula to find the distance Lee traveled. We can put this information into our formula: distance = rate ⋅ time. (This might seem excessive now, but it's a good habit for even simple problems and can make solving complicated problems much easier.) Here's what our table looks like: distance ![]() To keep track of the information in the problem, we'll set up a table. This diagram is a start to understanding this problem, but we still have to figure out what to do with the numbers for distance, rate, and time. You could picture Lee's trip with a diagram like this: The distance is unknown-it's what we're trying to find.The time is two-and-a-half hours, or 2.5 hours.Remember, we're looking for any information about distance, rate, or time. How far is the zoo from his house?įirst, we should identify the information we know. He drove an average speed of 65 mph, and it took him two-and-a-half hours to get from his house to the zoo. On his day off, Lee took a trip to the zoo. When you solve any distance problem, you'll have to do what we just did-use the formula to find distance, rate, or time. 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.Ħ0 ⋅ 0.5 is 30, so our distance would be 30 miles. 5 hours-that's the time.Īccording to the formula, if we multiply the rate and time, the product should be our distance.Īnd it is! We drove 50 mph for 0.5 hours-and 50 ⋅ 0.5 equals 25, which is our distance. You drove an average of 50 mph-that's the rate.You drove 25 miles-that's the distance.For an example of how this would work in real life, just imagine your last trip was like this: In other words, the distance you drove is equal to the rate at which you drove times the amount of time you drove. The relationship among these things can be described by this formula: To understand the difference among these, think about the last time you drove somewhere. There are three basic aspects to movement and travel: distance, rate, and time. But first, let's look at some basic principles that apply to any distance problem. In this lesson, you'll learn how to solve train problems and a few other common types of distance problems. 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. They involve a scenario in which you need to figure out how fast, how far, or how long one or more objects have traveled. en/algebra-topics/introduction-to-word-problems/content/ What are distance word problems?ĭistance word problems are a common type of algebra word problems.
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