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Employee 1

Earnings per Hour
Hours: 1, 2, 3
Earinings: 10, 20, 30

Employee 2:

0, 0
1, 15
3, 45
5, 75
What is the unit rate for earnings for Employee 1?
What is the unit rate for earnings for Employee 2?

1 answer

To find the unit rate for earnings for each employee, we will divide the total earnings by the total hours worked.

Employee 1:

  • Hours: 1, 2, 3
  • Earnings: 10, 20, 30

First, let's summarize the total earnings and total hours:

  • Total Earnings = \(10 + 20 + 30 = 60\)
  • Total Hours = \(1 + 2 + 3 = 6\)

Now, we calculate the unit rate:

\[ \text{Unit Rate} = \frac{\text{Total Earnings}}{\text{Total Hours}} = \frac{60}{6} = 10 \]

Employee 2:

  • Hours: 0, 1, 3, 5
  • Earnings: 0, 15, 45, 75

We will only consider the hours and earnings where the hours worked is greater than 0 for calculating the unit rate.

  1. For \(1\) hour, the earnings is \(15\).
  2. For \(3\) hours, the earnings is \(45\).
  3. For \(5\) hours, the earnings is \(75\).

Let's summarize the total earnings and total hours for the valid entries:

  • Total Earnings from valid entries = \(15 + 45 + 75 = 135\)
  • Total Hours from valid entries = \(1 + 3 + 5 = 9\)

Now, we can calculate the unit rate:

\[ \text{Unit Rate} = \frac{\text{Total Earnings}}{\text{Total Hours}} = \frac{135}{9} = 15 \]

Summary:

  • Unit Rate for Employee 1: \(10\) (dollars per hour)
  • Unit Rate for Employee 2: \(15\) (dollars per hour)