Easy algebra, what am I doing wrong?

Factual Questions
1

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?

2

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.

3

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

4

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

5

Thanks for the help. Got to remember to always make sure the units are correct.