325 meters in 28 seconds

Question

i need help with my math please please please please please please please please please please help me with it need a lot of help on the question

Answer 1

Hi Colette,

You didn't give us a question, just some numbers! Do you need help finding an average speed if something traveled 325 meters in 28 seconds? Let's try that.

First, and this is important for every question you'll ever have about speed: Remember that a speed is a distance per time, like "miles per hour" or "meters per second". Per means "in each" or "divided by". So "20 miles per hour" means something travels an average of 20 miles in each hour. It also means divide, so if a car travels 20 miles in 1 hour, that's 20 / 1 = 20 mph, or if it travels 40 miles in 2 hours, that's 40 / 2 or 20 mph (again, same speed).

Second, and just as important, the "per" means "divide" for the units too! Miles per hour (mph) means "miles traveled divided by the time taken". See that? 40 miles traveled in 2 hours means 40 / 2 = 20 miles per hour. Written a different way, that's:

40 miles

----------------- = 20 miles/hour

2 hours

20 mph = 20 miles per hour = 20 miles/hour (miles divided by hours)

I hope you have enough information now to calculate the speed in the question you didn't ask! If something travels 325 meters in 28 seconds, then that means:

325 meters

-------------------- = 11.6 meters/second or 11.6 m/s

28 seconds

Now that's often not enough to answer all the speed questions you'll get. For example, you might be asked to compare that speed to a car traveling 20 mph... which one is moving faster?

First we remember is #2 above... per means divide for units as well as the numbers. In fact, let's make this #3:

#3: If you divide units, you can cancel (remove) any units that are found on top and bottom of the equation. If you have seconds on top and you divide by seconds, you can eliminate seconds. Let's continue this example:

Using #3, let's convert 11.6 meters/second to a speed in units of miles/hour. We'll do it one step at a time, keeping track of units.

11.6 meters 60 seconds 60 minutes

-------------------- x ------------------ x ------------------ = 41,760 meters/hour

1 second 1 minute 1 hour

Wow, did you see that? Pay attention: Always, always make sure you write things out like this so that you can "cancel" identical units that are found on both top and bottom. To convert that speed of 11.6 m/s to meters/minute and then to meters per hour, you lay out those divisions and just multiply them all together. On the top it's 11.6 X 60 X 60 and on the bottom it's 1 X 1 X 1 = 1... we can ignore that 1 on the bottom and we strike out the units that are found both top and bottom and we end up with "meters" on the top and "hours" on the bottom, so we've converted to meters/hour. We kept the same units of distance, but changed the units of time.

But we need our speed in miles per hour, not meters per hour. To do that we need one more conversion, from meters into miles:

41,760 meters 3.28 feet 1 mile

------------------------ x ------------------ x ------------------ = 25.9 miles/hour

1 hour 1 meter 5280 feet

That's the conversion, but you have to pay attention to how we did that. In the first step we convert meters into feet... using a fraction of 3.28 feet per 1 meter. But how do we know to put feet on top and divide by meters? Why not put meters on top and divide by feet?? The secret is #3 above. We just set up our fractions (these are all fractions) so that the units we want to get rid of are found 1 on top and 1 on the bottom. At the first step we had feet on top, meters on bottom, giving us meters on both top and bottom... cancel them and we have feet left on top. In the second step we want miles on top, and get rid of feet so we multiply by the fraction 1 mile per 5280 feet. Cancel the feet from top and bottom and our final answer is 25.9 mph, miles per hour, miles / hour.

So whatever you wanted to ask about was traveling a little faster than the slow car going 20 mph that I used for an example. And now you know how to do almost every speed problem you'll run into. Remember those three key items and practice them in every speed problem:

1. Per means divide the numbers. Miles per hour means how many miles traveled divided by how many hours it takes.
2. Per means divide for the units too. Miles per hour means Miles divided by Hours.
3. Set up fractions to multiply so that the units you DON'T want are found on the top and the bottom so they can be canceled out. Then you just find conversion factors like 3 feet = 1 yard or 3.28 feet = 1 meter and use those as the fractions you need. Cancel out all the units you don't want, leave behind the units you DO want, and the problem will be all set up and will show the teacher (and your friends who need help) exactly how you solve the problem.

Hope that helps!

Paul