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

johnqwertyful
So is that 2 dollar/(mile/hour)=2 dollar hour/mile? What's a dollar hour? Is there a better way of handling this?

## Answers and Replies

Medicol
$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 ?

johnqwertyful
Science Advisor
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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?

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.

johnqwertyful
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.

Medicol
johnqwertyful
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?

Staff Emeritus
Science Advisor
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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.

Medicol
Mentor
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.

Medicol
zoobyshoe
$2 per mph is a miserable incentive to run faster. zoki85 And how much for walk? Science Advisor Homework Helper 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? Mentor 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!

Gold Member
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

Medicol