On a road trip, Andrew plans to use his cruise control for 125 mi, plus or minus 20 mi. Write and solve an equation to find the minimum and maximum number of hours for Andrew's road trip?

The correct answer is: Maximum number of hours Kennedy travels = 2.9 hours Minimum number of hours Kennedy travels = 2.1 hours

Hint:
|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by

We will construct an equation which models the situation with the help of the concept of absolute value.
Step by step solution:
Given,
Let the number of hours travelled be x
Cruising speed of Andrew’s car = 50 mi/h
Distance she plans to travel = 125 ± 20 mi
We know,
Speed =
The above equation can be rewritten as
Distance=Speed × Time
We form an equation in terms of distance travelled by the boat.
From the above relation, we have
Total distance travelled by the boat = 50x mi
Thus, the equation representing the given situation is
|50x - 125| = 20
We solve the above equation to get two values of x, which will be the minimum and maximum values  of x.
Using the definition of absolute value,

We get two possibilities,
For 50x - 125 < 0,
|50x - 125| = -(50x - 125) = 20
Simplifying, we get
-50x + 125 = 20
Subtracting 125 both sides, we have
-50x = 20 - 125 = -105
Dividing throughout by -50, we get
x =  = 2.1
For 50x - 125 ≥ 0,
|50x - 125| = 50x - 125 = 20
Adding 125 both sides, we get
50x = 20 + 125 = 145
Dividing by 25 throughout, we get
x = = 2.9
Hence, we get two values of x satisfying the given equation,
x = 2.1, 2.9
Thus,
Maximum number of hours Kennedy travels = 2.9 hours
Minimum number of hours Kennedy travels = 2.1 hours
Note:
Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.