Distance Traveled An athlete is 16 miles from home, running toward home at 6 miles per hour.
(a) Write a formula that calculates the distance D that the athlete is from home after x hours.
(b) Determine D when x = 1.5 hours.
(c) Find x when D = 5.5 miles. Interpret the result
D = 16 -6x
b) substitute 1.5 for x
c) substitute 5.5 for D
(a) To calculate the distance that the athlete is from home after x hours, we can use the formula:
D = 16 - 6x
(b) Let's substitute x = 1.5 into the formula:
D = 16 - 6(1.5)
D = 16 - 9
D = 7
Therefore, when x = 1.5 hours, the athlete is 7 miles from home.
(c) To find x when D = 5.5 miles, we need to solve the equation 5.5 = 16 - 6x for x.
First, let's isolate the variable by subtracting 16 from both sides:
5.5 - 16 = -6x
Simplifying the left side gives us:
-10.5 = -6x
Next, divide both sides by -6 to solve for x:
-10.5 / -6 = x
Thus, x = 1.75
Interpreting the result: When D = 5.5 miles, it means that the athlete is 5.5 miles away from home. The value of x = 1.75 indicates that it took the athlete 1.75 hours to reach that distance.