Question

a bicyclist is riding at a speed of 20mi/h when she starts down a long hill. The distance she travels in feet can be modeled by the function d(t)+= 5t^2 +20t, where t is the time in seconds.
a) The hill is 585ft long. How long will it take her to reach the bottom?
b) What if the hill were only half as long? How long would her ride take then?

Answer 1

a).
585= 5t²+20t
Subtract 585 to allow the equation to be equal to 0
5t²+20t-585=0
Solve the equation for x by factoring
5(t²+4t-117)=0
(t+13)(t-9)=0
t=9
9 seconds to reach the bottom

b). repeat the same process with your equation = 292.5
(292.5=5t²+20t)