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In case you are not familiar with translating word problems into equations please go through this post first: Information regarding the other two will be provided in the question stem. But how many of you truly understand what it signifies? My advice here, as usual, is to make sure you understand the concept behind the formula rather than just using it blindly.
If you travel at 50 mph for one hour, then you would have traveled 50 miles. If you travel for 2 hours at that speed, you would have traveled miles. If you were to double the speed, then you would have traveled miles in the first hour and miles at the end of the second hour.
We can figure out any one of the components by knowing the other two. For example, if you have to travel a distance of miles, but can only go at a speed of 50 mph, then you know that it will take you 2 hours to get there.
Supposing your friend told you that he was stuck in traffic along the way and that he traveled at 50 mph whenever he could move. Therefore, although practically he never really traveled at 25 mph, you can see how the standstills due to traffic caused his average to reduce.
Now, if you think about it, from the information given, you can actually tell how long he was driving and how long he was stuck due to traffic assuming; what is false but what they never worry about in these problems; that he was either traveling at 50 mph or 0 mph.
If he was traveling constantly at 50 mph, he should have reached in 2 hours. However, since he took 4 hours, he must have spent the other 2 hours stuck in traffic! Now lets see how we can represent this using the formula.
We know that the total distance is miles and that the total time is 4 hours.
However, can you see that no matter how many different rates he drove for various different time periods, his TOTAL distance depended simply on the SUM of each of the different distances he drove during each time period? Then if you speed up to 80 mph for another half hour, you will cover 40 miles, and then if you slow down to 30 mph, you will only cover 15 miles in the next half hour.
It is fairly easy to see this looking at it this way, but it is more difficult to see it if we scramble it up and leave out one of the amounts and you have to figure it out going "backwards".
That is what word problems do.
Further, what makes them difficult is that the components they give you, or ask you to find can involve variable distances, variable times, variable speeds, or any two or three of these. You have to think about how to use the formula.
ONCE the conditions deal with different speeds or different times, you have to look at each of those components and how they go together. And that can be very difficult if you are not methodical in how you think about the components and how they go together.
The formula doesn't tell you which components you need to look at and how they go together. For that, you need to think, and the thinking is not always as easy or straightforward as it seems like it ought to be.
In the case of your friend above, if we call the time he spent driving 50 mph, T1; then the time he spent standing still is 4 - T1 hours, since the whole trip took 4 hours. And, since the time he spent going zero is 4 - 2it also turns out to be 2 hours.
Sometimes the right answers will seem counter-intuitive, so it is really important to think about the components methodically and systematically. There is a famous trick problem: To qualify for a race, you need to average 60 mph driving two laps around a 1 mile long track.
You have some sort of engine difficulty the first lap so that you only average 30 mph during that lap; how fast do you have to drive the second lap to average 60 for both of them? Intuitively it would seem you need to drive 90, but this turns out to be wrong for reasons I will give in a minute.Edraw is used as a comparison chart software coming with ready-made comparison chart templates that make it easy for anyone to create great looking comparison chart.
A business email is written and sent for several different purposes. It is an effective tool for communication in which information may easily be distributed through a single click of a button. If you'd rather do a business plan presentation than a Word doc, you can download one of Microsoft Office's half a dozen or so PowerPoint templates for just that purpose.
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