Roma sherry drove 80 miles from her home town to her parents' town. during her return trip, she was able to increase her speed by 44 miles per hour. if her return trip took 1 hour less time, find her original speed and her speed returning home.

Roma Sherry drove 330 miles from her hometown to Tucson. During her return trip, she was able to increase her speed by 11 mph. If her return trip took 1 hour less time, find her original speed and her speed returning home. : Let s = original speed then (s+11) = return speed : Write a time equation: Time = distance%2Fspeed : Original time = return time + 1 hr 330%2Fs = 330%2F%28%28s%2B11%29%29 + 1 : Multiply equation by s(s+11) and you have: 330(s+11) = 330s + s(s+11) : 330s + 3630 = 330s + s^2 + 11s : 0 = 330s - 330s + s^2 + 11s - 3630 : A quadratic equation: s^2 + 11s - 3630 = 0 Factor this to: (s + 66)(s - 55) = 0 Positive solution s = 55 mph is original speed. : Find the time 330/55 = 6 hr, original time and 330/66 = 5 hrs, faster time; confirms our solution.