Question 547045: a cheetah was timed running 200 yards in 6 seconds. What was its average speed in miles per hour?
I am a mom trying to help my daughter with her math homework. Not sure where to begin with this. Do I divide 200 by 6? but then what? I need help!! Could you show me what the problem should look like? Thanks!! Amy
Found 2 solutions by mananth, bucky:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! a cheetah was timed running 200 yards in 6 seconds. What was its average speed in miles per hour?
you must first do the conversion from yards/second to miles/hour.
Then your problem is solved.
1 yard = 3 feet
600 yards=1800feet
1800 feet in 6 seconds
so in 1 second the cheetah runs
1800/6 = 300 feet /second
....
convert 300 feet/second to miles /hour
1 mile = 5280 feet
1 second = 1/3600 hour ( 3600 seconds ,ake an hour)
300 feet = 300/5280 miles
1 second = 1/3600 hour
=204.5 mph
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! Thanks for helping your daughter with math.
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The hardest part of this problem involves translating units. You were correct in your initial plan to divide 200 by 6. The 200 is in units of yards and the 6 is in units of seconds. So when you do that division, your answer will have units of yards per second. But the problem asks for the answer in miles per hour and here the "fun" begins. How do you get from yards per second (which means units of yards divided by units of seconds) to miles per hour?
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The process that I'm about to describe will seem complex, but with a little thought and practice, it's not too bad. The big advantage is that it helps to show you what you need to do, and it helps to ensure that you don't mess up on the conversions that you need to do.
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Start by writing down the units at the beginning. In this case you are beginning with yards per second as follows:
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Next, write down the units that you want to get to. In this problem it is miles per hour as follows:
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Some how we need to convert yards into miles and seconds into hours. There are 1760 yards in a mile. To cancel out the yards units in the cheetah's speed, we need to multiply in by a units factor that has yards in the denominator and the corresponding miles in the numerator. So going back to the cheetah's speed in yards per second we can multiply it by the conversion factor as below:
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Notice that after we do that multiplication the unit yards in the numerator will cancel with the units yards in the denominator and we will be left with units of miles per second.
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Now we need to get rid of the seconds by converting it to hours. In our units equation we have seconds in the denominator so we need a multiplier to cancel it out by having seconds in the numerator. There are 3600 seconds per hour (60 seconds in a minute times 60 minutes in an hour equals 3600 seconds per hour.)
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So in the conversion arrangement that we have started, let's add another multiplier that will cancel the seconds and introduce the hours. This is shown below:
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Now let's add to this arrangement the conversion numbers. The cheetah's speed is 200 yards in 6 seconds. Put that in:
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Next, 1 mile is 1760 yards. Put that in:
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Finally 3600 seconds is 1 hour. Put that in:
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Cross out any units that appear in both the numerator and the denominator:
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Note that the only units that are left are miles and hour. Now all we have to do is multiply the numbers in the numerator (200 times 1 times 3600) and divide that answer by the numbers multiplied in the denominator (6 times 1760 times 1). With the cancellation of the units, you are left with:
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The numerator becomes 
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And the denominator becomes 
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Divide the 720,000 by 10,560 and you get 68.1818 miles/hour. That's about the right speed for a cheetah. They can sprint around 70 miles per hour, so our answer is around what it should be.
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If your daughter takes physics in high school, she will be involved with a lot of problems that have unit conversions such as this one. This method of working conversions will come in handy and help to do the conversions correctly.
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I hope this wasn't too confusing. As I said, with a little thought and practice it gets easier.
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Good luck and thanks again for helping your daughter. Hopefully this site will assist you in doing that for her.
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