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

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In summary, the conversation is discussing the payment system of $2 for every mile per hour and the confusion surrounding the units and calculations. The equation A = 2$/mph * (miles/hour) = 2$ hour/mile is proposed to understand the payment structure.
  • #1
johnqwertyful
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So is that 2 dollar/(mile/hour)=2 dollar hour/mile? What's a dollar hour? Is there a better way of handling this?
 
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  • #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.
And
Given $2 for 1 mile per 1 hour,
now $1 for x mile(s) per y hour(s) means ?
 
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  • #3
johnqwertyful said:
So is that 2 dollar/(mile/hour)=2 dollar hour/mile? What's a dollar hour? Is there a better way of handling this?

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.
 
  • #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.
 
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  • #5
phinds said:
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.
But how do the units work out? Is "mph" now somehow an irreducible unit?
 
  • #6
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.
 
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  • #7
johnqwertyful said:
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.
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.
 
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  • #8
$2 per mph is a miserable incentive to run faster.
 
  • #9
And how much for walk?
 
  • #10
johnqwertyful said:
So is that 2 dollar/(mile/hour)=2 dollar hour/mile? What's a dollar hour? Is there a better way of handling this?

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?
 
  • #11
BobG said:
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?
I took it as the second one and was hoping to make $20 that way!
 
  • #12
johnqwertyful said:
So is that 2 dollar/(mile/hour)=2 dollar hour/mile? What's a dollar hour? Is there a better way of handling this?
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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1. Is this a legitimate offer?

Yes, this is a legitimate offer. It is a simple experiment to measure your running speed and offer a reward for your performance.

2. How will the payment be made?

The payment will be made in cash or through a digital payment method, depending on your preference.

3. Are there any restrictions on the running surface?

The running surface should be flat and even to ensure accurate measurement of your speed. It should also be a safe and suitable surface for running.

4. Do I have to run at a certain time or place?

No, you can choose the time and place for the run as long as it meets the requirements of a flat and safe surface.

5. Is there a limit to the number of attempts?

No, there is no limit to the number of attempts. You can make multiple attempts to improve your speed and earn more money.

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