However, we do know that the Platters drove 15 mph faster than the Hills. In any case, we're trying to find out how far Bill drove on the interstate, so let's represent this number with d. If the interstate distance is d, it means the in-town distance is a number that equals the total, 225, when added to d. In other words, it's equal to 225 - d. We can use the same technique to fill in the time column. The equation for Jon's travel is d = 65t. 4. What time does the second train catch up to the first? 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. The equation for the Platter family's trip is d = (r + 15) ⋅ 13. The final type of distance problem we'll discuss in this lesson is a problem in which one moving object overtakes—or passes—another. And if you know the time and distance a passenger traveled on a plane, you could quickly figure the distance she traveled simply by reconfiguring the formula. See? 1. The other equation, which describes the slow train, can't be solved alone either. Write two expressions for that quantity, one using each "traveler." Our next step is to group like terms—remember, our eventual goal is to have t on the left side of the equals sign and a number on the right. We can get rid of 60t on the right side by subtracting 60t from both sides: 80t - 60t is 20t. Just remember to pay special attention when you're setting up your chart. Time = 4 hours. Bill took a trip to see a friend. 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. Print the PDF: Distance, Rate, Time Worksheet No. The Hill family's trip can be described by d = r ⋅ 16. You can even use it to solve certain problems where you're trying to figure out the distance, rate, or time of two or more moving objects. Distance is the length of space traveled by a moving object or the length measured between two points. When solving distance problems, explain to students that they will use the formula: or rate (speed) times time equals distance. One train is moving at a speed of 45 mph, and the other is moving 60 mph. Find the speed of the current. First, let's fill in the values we know. Solving distance problems. But what about our other equation, the one for in-town travel? Pawnee and Springfield are 420 miles apart. This problem is asking you to calculate how long it will take these two trains moving toward each other to cross paths. 65 ⋅ 2.5 equals 162.5. If you work either equation on its own, you won't be able to find a numerical value for d. In order to find the value of d, we'll also have to know the value of t. We can find the value of t in both problems by combining them. Even though the trip described in this problem is slightly different from the one in our first problem, you should be able to solve it the same way. How far could we drive in 30 minutes? Create a Distance, Rate, and Time chart similar to the one shown below. For our fast train, the equation would be d = 60 ⋅ 4. Example 2 –On the first part of her trip Natalie road her bike 16 miles and on the second part of her trip she road her bike 42 miles. The equation for the fast train isn't solvable on its own, but it does tell us that d is equal to 60t. The problem gives us the speed of each train. So t is equal to 3. See if you can solve it on your own. When we replace the d in that equation with 70t, the equation suddenly gets much easier to solve. So t is equal to 3. The rate is the speed at which an object or person travels. Now we just need to get rid of the coefficient next to t. We can do this by dividing both sides by 105. Next, let's cancel out the 225 next to 70t. For an example of how this would work in real life, just imagine your last trip was like this: According to the formula, if we multiply the rate and time, the product should be our distance. Here's a typical overtaking problem: The Hill family and the Platter family are going on a road trip. Substituting 70t for d in our equation for interstate travel won't help us find the value of t—all it tells us is that 70t is equal to itself, which we already knew. When you solve any distance problem, you'll have to do what we just did—use the formula to find distance, rate, or time. The equation for Dani's travel is 270 - d = 70t. How long will they travel before they meet? When you're finished, scroll down to see the answer and an explanation. When you're finished, scroll down to see the answer and an explanation. An intersecting distance problem is one where two things are moving toward each other. In other words, the time it takes the trains to meet is 4 hours. When you solve any distance problem, you'll have to do what we just did—use the formula to find distance, rate, or time. To solve this problem, we'll need to combine the equations. This website uses cookies to measure and analyze our traffic.
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