the unit rate of employee 1's earnings are every 1 hour 10 earnings

Question

the unit rate of employee 2's earnings are every 1 hour 15 earnings

What is the equation that represents the proportional relationship between the earnings and hours worked for Employee 1 and Employee 2?

Answer 1

To create the equations representing the proportional relationship between earnings and hours worked for Employee 1 and Employee 2, we first need to understand the given unit rates.

1. Employee 1:

   • Unit rate: 10 earnings per hour.
   • Let \( x \) represent the number of hours worked.
   • The equation for Employee 1 can be written as: \[ E_1 = 10x \] where \( E_1 \) is the total earnings of Employee 1.

2. Employee 2:

   • Unit rate: 15 earnings per hour.
   • Let \( y \) represent the number of hours worked.
   • The equation for Employee 2 can be written as: \[ E_2 = 15y \] where \( E_2 \) is the total earnings of Employee 2.

In both cases, the earnings are directly proportional to the number of hours worked.

So, the two equations representing the proportional relationships for Employees 1 and 2 are:

1. For Employee 1: \( E_1 = 10x \)
2. For Employee 2: \( E_2 = 15y \)

If you want to express the relationship in a single format using a common variable for hours worked (let's say \( h \)), you could let \( x = h \) and \( y = h \) but keep in mind that they may work different hours. However, these equations accurately capture how their earnings are related to the hours they work.