Algebra 2 word problem

Question

In a 200 mile bike ride, Duva realized that if she could average 1 mile per hour faster than she did on her last 200 mile ride, she would finish 1 hour sooner.  How long did she spend on her last 200 mile ride?

Answer 1

distance = rate of speed times time

r=d/t = 200/t

200 = rt = (r+1)(t-1)

(r+1)(t-1) = 200

r+1 = 200/(t-1)

r = 200/(t-1)-1

200/t = 200/(t-1) - 1

multiply by t(t-1)

200(t-1) = 200t -(t(t-1))

200t - 200 = 200t -t^2 +t

t^2 -t -200 = 0

t = (1/2) + (1/2)sqr(1+800)

t = 14.651 hours on her last 200 ride

= about 14 hours and 39 minutes

r=13.651 mph on her last 200 ride

if she goes 14.651 mph, it will take her 13.651 hours, one hour less if she goes 1 mph faster