You are paid $78 for 6 and a half hours of work. what is your rate of pay?

The most important part of the problem lies in the fact that the hours have to be converted to minutes before starting to solve the problem.
1 hour = 60 minutes
6 and half hours = (6 * 60) + 30 minutes
                           = 360 + 30
                           = 390 minutes
So the payment for 390 minutes is = 78 dollars
Then
The payment for 60 minutes = (78/390) * 60
                                               = 2 * 6 dollars
                                               = 12 dollars
So the rate of pay given is $12 per hour. I hope the procedure is easy enough for you to understand. You can always use this method for solving similar type of problems.