# Easy algebra, what am I doing wrong? **URL:** \ **Category:** Factual Questions\ **Created:** [April 15, 2005, 3:17am UTC](https://boards.straightdope.com/t/easy-algebra-what-am-i-doing-wrong/299426 "2005-04-15T03:17:36Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [April 15, 2005, 3:17am UTC](https://boards.straightdope.com/t/easy-algebra-what-am-i-doing-wrong/299426/1 "2005-04-15T03:17:36Z")
I know I am missing something really simple here. I just can’t figure out what. Sally drives 30 minutes to work each day. If she increases her speed by 10 mph she gets there 6 minutes earlier. (x)(30/x) = (x + 10)(24/x) 30 = (x^2 +10x)(24) 24x^2 +240x -30 =0 4x^2 +40x -5 = 0 This does not factor. What did I do wrong? ---
**Author:** ![Greg\_Charles](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)\ **Post date:** [April 15, 2005, 3:29am UTC](https://boards.straightdope.com/t/easy-algebra-what-am-i-doing-wrong/299426/2 "2005-04-15T03:29:46Z")
You mixed units. The time is measured in minutes. The extra speed is measured in miles per hour. You’ve got to convert one or the other to have a consistent equation. My answer is she normally goes 40 miles per hour for 20 miles. If she goes 50 mph she will arrive in 24 minutes. ---
**Author:** ![Greg\_Charles](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)\ **Post date:** [April 15, 2005, 3:34am UTC](https://boards.straightdope.com/t/easy-algebra-what-am-i-doing-wrong/299426/3 "2005-04-15T03:34:52Z")
For that matter, I didn’t need to go all quadratic. I converted 30 minutes to 1/2 hour and 24 minutes to 2/5 hour. Let s = speed. That gives: s/2 = 2(s+10)/5 5s = 4(s+10) (cross multiply) 5s = 4s + 40 s = 40 ---
**Author:** ![wolf\_meister](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolf_meister/32/15202_2.png) [@wolf\_meister](https://boards.straightdope.com/u/wolf_meister)\ **Post date:** [April 15, 2005, 6:22am UTC](https://boards.straightdope.com/t/easy-algebra-what-am-i-doing-wrong/299426/4 "2005-04-15T06:22:10Z")
To show this algebraically: Let D be the distance (miles) and let V be the _original_ velocity (mph) and the time would be measured in hours. (30 minutes = .5 hours and “6 minutes earlier” is 24 minutes which equals .4 hours. We define distance as velocity \* time. Therefore, D = V \* .5 (at original velocity) D = (V + 10) \* .4 (at 10 mph faster) .5V = .4V + 4 .1 V = 4 Velocity = 40 mph D = 40 mph \* .5 hours D = 20 miles ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [April 15, 2005, 1:16pm UTC](https://boards.straightdope.com/t/easy-algebra-what-am-i-doing-wrong/299426/5 "2005-04-15T13:16:34Z")
Thanks for the help. Got to remember to always make sure the units are correct.