If you increase your rate by 25 mph and you are going 25 mil

If you increase your rate by 25 mph and you are going 25 miles you get there 10 min earlier, what was your initial rate?

Solution

d = rt
25 = rt
25 = (r+25)*(t- 1/6) [10 mins = 1/6 hour]
rt = (r+25)*(t- 1/6) = rt + 25t - r/6 - 25/6
6rt = 6rt + 150t - r - 25
150t = r+25
r = 25/t
150t = (25/t) + 25
150t^2 = 25 + 25t
6t^2 - t - 1 = 0
(3t + 1)*(2t - 1) = 0
t = 1/2 hour (Ignore negative solution)
r = 50 mph