A runner steadily increases her speed for the first 45 minut

A runner steadily increases her speed for the first 4.5 minutes, runs at a 10 mph for 15.5 minutes, and then steadily slows to a stop in 3 minutes. What kind of function does this represent? Here is the graph for the runner\'s speed. Write the function R(m) for this graph. At what rate did the runner increase her speed? What is R(21) and what does it represent in terms of the runner?

Solution

a) this function is a piecewise function

first it is linear ( positive slope ) then constant and again linear ( negative slope )

b) R(m)

for 1st part function is

y = 120 t   if t 0<= t < 4.5 minutes

for constant part function is

y = 10 if 4.5 <= t <= 20

for decreasing part

y = -195t+75 , 20 < t <= 23

therefore, R(m) = { y =120t   if t 0<= t < 4.5 minutes

                            y = 10 if 4.5 <= t <= 20

                            y = -195t+75, 20 < t <= 23 }

c) rate at which runner increase her speed = slope of first function that is 120 miles / hour^2

d) R(21) = -195(21/60) + 75 = 6.75 miles / hour

it represents the speed of runner at 21 minutes