Respuesta :
t(r) = 15/r
We start out with the formula for distance, d = rt, where d is the distance, r is the rate (speed), and t is the time. We know the distance is 15 miles:
15 = rt
We want this as a function of the speed; this means we want speed to be the independent variable and time to be the dependent. We cancel the r away from t by dividing:
15/r = rt/r
15/r = t
Now we write it in function notation:
t(r) = 15/r
We start out with the formula for distance, d = rt, where d is the distance, r is the rate (speed), and t is the time. We know the distance is 15 miles:
15 = rt
We want this as a function of the speed; this means we want speed to be the independent variable and time to be the dependent. We cancel the r away from t by dividing:
15/r = rt/r
15/r = t
Now we write it in function notation:
t(r) = 15/r
Average speed of a body is the speed by which the same amount of distance covered by the body in each time interval. The formula that describes the time as the function of the average speed for the given problem is,
[tex]t(s)&=\dfrac{15}{s} [/tex]
Given information-
The distance of the hike is 15 miles.
The time needed for a 15 miles long hike depends on the average speed.
Average speed-
Average speed of a body is the speed by which the same amount of distance covered by the body in each time interval. It can be given as the ratio of total distance covered by a body in the time span.
Thus the average speed [tex]s[/tex] of a body is,
[tex]s=\dfrac{d}{t} [/tex]
Here d is the distance covered by the body and t is the time taken by the body.
Rewrite the above equation for the time [tex]t[/tex],
[tex]\begin{aligned}\\ ts&=d\\ t&=\dfrac{d}{s} \\ \end[/tex]
Put the value of distance,
[tex]t&=\dfrac{15}{s} [/tex]
Thus the time in inversely proportional to the average speed of the body. Write the above equation in the function of average speed form as,
[tex]t(s)&=\dfrac{15}{s} [/tex]
Hence, the formula that describes the time as the function of the average speed for the given problem is,
[tex]t(s)&=\dfrac{15}{s} [/tex]
Learn more about the average speed here;
https://brainly.com/question/21118876
