The time Hazel spends commuting to work can be represented by two expressions:

Time to work: [tex]x + 6y[/tex]
Time from work: [tex]3x - 10y[/tex]

Which expression represents the total time Hazel spends commuting to and from work each day?

A. [tex]7x - 7y[/tex]
B. [tex]4x - 4y[/tex]
C. [tex]4x + 4y[/tex]
D. [tex]4x - 16y[/tex]



Answer :

To determine the total time Hazel spends commuting to and from work each day, we need to add the expressions for the time to work and the time from work.

Given:
- Time to work: [tex]\( x + 6y \)[/tex]
- Time from work: [tex]\( 3x - 10y \)[/tex]

Step-by-Step Solution:

1. Write down the expressions for time to work and time from work:
- Time to work: [tex]\( x + 6y \)[/tex]
- Time from work: [tex]\( 3x - 10y \)[/tex]

2. Add the two expressions to find the total commuting time:
[tex]\[ \text{Total commuting time} = (x + 6y) + (3x - 10y) \][/tex]

3. Combine like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( x + 3x = 4x \)[/tex]
- Combine the [tex]\( y \)[/tex] terms: [tex]\( 6y - 10y = -4y \)[/tex]

4. Write the simplified expression:
[tex]\[ \text{Total commuting time} = 4x - 4y \][/tex]

Thus, the expression that represents the total time Hazel spends commuting to and from work each day is [tex]\( 4x - 4y \)[/tex].

Therefore, the correct choice is:
[tex]\[ \boxed{4x - 4y} \][/tex]