Question

The length in miles of two highways after 10 years of construction can be modeled by expressions. For highway A, the expression is 20t + 150. For highway B, it is 15t + 175. Write an expression that shows the difference in length between the two highways.

Answer 1

The difference in length between highway A and highway B after 10 years can be expressed as 5t - 25 miles, where t represents the number of years.

Step-by-step explanation:

To find the expression that shows the difference in length between the two highways after 10 years of construction, we subtract the expression representing the length of highway B from the expression representing the length of highway A. The expression for highway A is 20t + 150 miles and for highway B it is 15t + 175 miles. The difference can be found by performing the subtraction (20t + 150) - (15t + 175).

So the expression representing the difference in length between the two highways is:

20t + 150 - (15t + 175) = 5t - 25

This means that after 10 years, highway A will always be 5t - 25 miles longer than highway B, where t represents the number of years.