Are you sure you want to delete this answer? Yes Sorry, something has gone wrong. While I teach in elementary, we use a strategy to help distinguish important information from the "trash," or info that we don't need. It can be applied to any word problem at any level to make everything easier to understand.
Time So rate is defined as distance divided by time, which is a ratio. Speed is another word that is used for rate.
When a problem says that a train is moving at a speed of 40 mph, you can understand this to mean that the train's rate is 40 mph, which means it will travel 40 miles in one hour. Here are two different ways to approach this problem. Let's start by listing the information given: Speed of Train A: We'll use the notion of relative speed 1 or relative rate in order to express the rates of the two trains in one number that can then be used in the distance formula.
Imagine you're on Train A. You're going 70 mph, so your speed relative to the trees, houses, and other non-moving things outside the train is 70 mph. All of those objects look as if they're going by at 70 mph. Now imagine you're the engineer and you can see Train B coming toward you - not on the same track, of course!
Since Train B is moving 60 mph, it will look as if it's approaching faster than if it were sitting still in the station - a lot faster than the trees and houses appear to be moving.
The relative speed of the two trains is the sum of the speeds they are traveling. If you're on either of the trains, this is the speed you appear to be moving when you see the other train.
What if the trains were traveling in the same direction? Then we'd need to subtract the speed of the slower train from the speed of the faster train, and their relative speed would be 10 mph. At this point we know two of the three unknowns: We find that the trains meet two hours after leaving their respective cities.
Here we'll begin by noting that the distance between Westford and Eastford is miles: Now, where do the trains meet? We again use the distance formula to find how far each train has traveled in two hours: To check this, we can add to Let's look at a variation on this problem.
Train A, traveling 40 mph, leaves Westford heading toward Eastford, miles away. When do the two trains meet? Notice that in this problem, the two trains do not leave their respective cities at the same time. Let's move the starting point for Train A so we can treat the problem as if the trains leave at the same time, which we already know how to do.
We know that Train A is moving 40 mph, and will therefore travel 40 miles in the hour before Train B leaves Eastford. Since t represents the time traveled by each train after Train A has already traveled for one hour, Train B travels 2 hours before meeting Train A.
Let t represent the time that Train A travels. Again, the sum of the distances traveled by the two trains up until the time they meet is miles:Actually plugging in your answer requires you to go through the algebra manipulations in the problem.
You add, subtract, multiply, and divide to see if you get a true statement using your answer. For example, you need to perform the operations in the following equation . Take a break. Let's see what else you know. Back to practice. Algebra 1 O.2 Word problems with money.
Algebra is a powerful tool for problem solving in science, engineering, economics, finance, architecture, ship-building and many other day-to-day tasks. If we didn't use letters in place of numbers (and used words instead), we would be writing many pages for each problem and it would be much more confusing.
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I believe we’re teaching students how to think, how to approach difficult problems, and that math happens to be the best way to do so for many people. Math is a complicated discipline, and while some problems are routine and straightforward, some problems require zigzag mazes and long expositions of solutions before an answer can be found.
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