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I offer to pay you 2 dollars for every mph you can run

  1. Oct 8, 2014 #1
    So is that 2 dollar/(mile/hour)=2 dollar hour/mile? What's a dollar hour? Is there a better way of handling this?
  2. jcsd
  3. Oct 8, 2014 #2
    $2 for every mph ? Whether it is $2 either for the speed or for the distance or for the hours is confusing. But yours is for the speed, which sounds odd if applied to humans.
    Given $2 for 1 mile per 1 hour,
    now $1 for x mile(s) per y hour(s) means ?
  4. Oct 8, 2014 #3


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    You are over thinking it. It's just $2 per mph, so if I can run 12mph, which the latest marathon world record setter did recently, then you own me $24.
  5. Oct 8, 2014 #4
    Well to manipulate naively, 1 dollar/(x mile/y hour)=y hour dollar/x mile=y/x hour dollar/mile so we are at the first question.

    However, with this you run into a problem. If you run 1 mile per 4 hours, you would run 4 times as slowly as someone who ran 1 mile per 1 hour, but you would get paid 4 times as much.
  6. Oct 8, 2014 #5
    But how do the units work out? Is "mph" now somehow an irreducible unit?
  7. Oct 8, 2014 #6


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    Obviously, if the rate of pay is $2 / mph, or to put it $2 * hour / mile, I want to figure out how much I get paid if I run 1 mile in 4 hours, so I have to cancel hours and miles to leave $. Thus, the payout = ($2 * hour / mile ) * (1 mile) / (4 hours) = $0.50, which is the same as calculating the average speed of the run = 1 mile / 4 hours = 1/4 mph and then multiplying by the rate of $2 / mph.

    There's nothing mysterious about this: it's straightforward algebra, often the most difficult, yet essential math subject.
  8. Oct 8, 2014 #7


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    The unit is $/mph. The others are either gibberish or just plain wrong. You are trying to attach meaning to them, but they do not have the meaning you are attaching to them. IE: 1 mile per 4 hours is 1/4 mph and gets you paid $.50. Your alternative is just plain wrong. By flipping-over the mph to make h/mi, you are getting rid of the "per" while pretending not to.
  9. Oct 8, 2014 #8
    $2 per mph is a miserable incentive to run faster.
  10. Oct 8, 2014 #9
    And how much for walk?
  11. Oct 8, 2014 #10


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    I take it you mean you'll pay $2 for every mile a person can run in one hour?

    In other words, you're not going to pay Usain Bolt $50 for running 100 meters in 8.95 seconds?
  12. Oct 8, 2014 #11


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    I took it as the second one and was hoping to make $20 that way!
  13. Oct 8, 2014 #12
    Make an equation out of itto see whatt is going on.
    One interpretation is:
    A - Amount you will receive
    R - rate , in this case 2$/mph
    V - Variable, in this case the value in mph that you are doing.
    A = R V
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