Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.

Which equation represents the relationship between d
, the number of dollars Rajindri earns, and t
, the amount of time Rajindri works, in hours?

1 answer

Rajindri earns $163 for every 2 hours she works. To find the equation that expresses the relationship between her earnings (d in dollars) and the time worked (t in hours), we can establish a couple of steps.

  1. First, we determine her hourly rate. Since she earns $163 for every 2 hours, we can divide her earnings by the time to find her rate per hour:

    \[ \text{Hourly Rate} = \frac{163}{2} = 81.5 \text{ dollars per hour} \]

  2. Now we can set up the equation representing the total earnings based on the hours worked. If she earns $81.5 for each hour worked, then for t hours the equation for her earnings will be:

    \[ d = 81.5t \]

Alternatively, if we are to maintain the original relation of her earnings over time worked of 2 hours, we can express it as:

\[ d = \frac{163}{2} t \]

In this case, since every 2 hours yields $163, the equation can also be represented as:

\[ d = 81.5t \]

Both equations are equivalent and represent the same relationship. Therefore, the equation that represents the relationship between dollars earned (d) and hours worked (t) is:

\[ d = 81.5t \]