To determine the total time Hazel spends commuting to and from work each day, let's break down the problem step by step.
First, let's figure out the expressions given for her commute:
- Time to work: [tex]\( x + 6y \)[/tex]
- Time from work: [tex]\( 3x - 10y \)[/tex]
To find the total time Hazel spends commuting each day, we will need to add these two expressions together:
[tex]\[
\text{Total time} = (\text{Time to work}) + (\text{Time from work})
\][/tex]
Substituting the given expressions:
[tex]\[
\text{Total time} = (x + 6y) + (3x - 10y)
\][/tex]
Next, we will combine the like terms. Let's first combine the [tex]\( x \)[/tex] terms:
[tex]\[
x + 3x = 4x
\][/tex]
And now combine the [tex]\( y \)[/tex] terms:
[tex]\[
6y - 10y = -4y
\][/tex]
So, adding the results together, we have:
[tex]\[
\text{Total time} = 4x - 4y
\][/tex]
Therefore, the expression that represents the total time Hazel spends commuting to and from work each day is:
[tex]\[
4x - 4y
\][/tex]
The correct choice from the given options is:
[tex]\[
4x - 4y
\][/tex]
