The minimum and maximum time for the object to travel 30 feet at a speed of 10 ft/s is 3 seconds.
How to determine the minimum and maximum times
To determine the minimum and maximum times for an object to travel a distance of 30 feet at a speed of 10 ft/s, set up an absolute value equation.
Let's denote the time it takes for the object to travel the distance as t.
The distance traveled by the object is given by the formula:
Distance = Speed * Time
In this case, the distance is 30 feet, and the speed is 10 ft/s.
Thus, we have:
30 = 10t
To find the minimum and maximum times, consider the absolute value of the expression 10t.
The absolute value of a number represents its distance from zero on a number line, always resulting in a non-negative value.
Therefore, our absolute value equation becomes:
|10t| = 30
To solve this equation, we can split it into two cases:
Case 1: 10t = 30
Solving for t:
t = 3
Case 2: -(10t) = 30
Solving for t:
-10t = 30
Dividing by -10 (note that dividing by a negative number flips the inequality):
t = -3
However, since time cannot be negative in this context, we discard the second case.
Therefore, the minimum time for the object to travel 30 feet at a speed of 10 ft/s is 3 seconds.