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

$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 ?

 

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.

 

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.

 

$2 per mph is a miserable incentive to run faster.

 

And how much for walk?

 

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?

 

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