I just baked a lot of buns. Would you mind bringing them to restaurants around the city? Do you think you can do it quickly? Great, you are hired. These buns taste best within an hour of coming out of the oven. That means I would really like you to get them to the restaurants in the next sixty minutes. The restaurants are spread all across the city. Some of them are close together. Others are far apart. You will be able to drive quickly on some streets. There will be a lot of cars on others, and you will have to go slowly. But if you can go five miles in one hour, the buns will still taste great. Ready? Go!
I better get ready. These are almost done.
Whenever you need to go somewhere, such as a lot of different restaurants, it's good to know how much time you have to get there. Right now, you have one hour. A time interval
is one section of time from start to finish. It can be anywhere from five minutes to 500 years. The trips from one restaurant to the next will have different time intervals. It might only take you 2 minutes to get from this restaurant to that one. But it could take you twenty minutes to get to the one after that. Only 38 minutes left. Better step on it.
You also need to consider how far you need to travel. Five minutes can be a lot of time or not enough, depending on how far you have to go. A distance interval
is one section of space from start to finish. Just like time, it can be many different sizes. It could be five inches or it could be 500 miles. Lucky for you, the space you have to cover in an hour is only five miles. Hand off those buns. No time to listen to the customers enjoy them.
I don't think this restaurant is going to need many buns.
So far you have gone two miles. You had better check how much time you have left. Only thirty minutes! Because of the cars and dogs and other things that got in your way, you are not even halfway there, even though half of the time is gone. When time has passed, we say it has elapsed
. Right now, thirty minutes have elapsed. You still have three miles left to go. Those buns are getting cold.
How am I ever going to get through this crowd!
Now you are zooming to each restaurant. When you first started you believed that you had lots of time, but because of all the cars, you had to go slowly. So now you need to make up time with more speed. Average speed
means your speed from start to finish, when we put all of your different speeds together. It is not how fast you are going at any one second, but your speed over a longer time. Sometimes you were driving slowly and sometimes quickly. Average speed is a measurement of the speed you went the whole time you were moving and is somewhere between all the ups and downs. Make sense? No? Then let's zoom to the next paragraph.
In order to get all of these buns out, you could drive five miles per hour for the hour and have an average speed of 5 mph. Or you could drive nowhere for half an hour and then drive ten miles per hour for the last half hour. This would still have an average of five. That's because average speed = d/t
, or distance divided by time. You can make up for your slow start by driving fast to the last two places. Oh, just make sure you slow down enough to hand people their buns. No one likes a bun in the face.
Nobody likes a pie in the face either.
After you have taken all of the buns to the restaurants, you screech to a stop in front of my bakery. I am holding a watch. I see that all the buns are gone. One hour has elapsed. You had a time interval of one hour and a distance interval of five miles. By dividing the five miles by the hour you were gone, I can tell that you got the buns to the restaurants in time for them to still taste great! Here, have a free bun! Oh, it doesn't taste fresh? Well, enjoy the taste of a job well done.References:
Internet 4 Classrooms. "Elapsed Time Resources" Internet 4 Classrooms, 2011. <http://www.internet4classrooms.com/elapsed-time.htm