Question 499020
By increasing his usual speed by 25 kilometers per hour, a bus driver decreases the time on a 25-kilometer trip by 10 minutes.
 Find the usual speed.
:
Let s = his usual speed
Change 10 min to 1/6 hr
write a time equation; time = dist/speed
Usual time - 10 min = faster time
{{{25/s}}} - {{{1/6}}} = {{{25/((s+25))}}}
multiply by 6s(s+25), results
6(s+25)*25 - s(s+25) = 6s*25
150(s+25) - s^2 - 25s = 150s
150s + 3850 - s^2 - 25s = 150s
Combine as a quadratic equation on the right
0 = s^2 + 25s - 3750
Factors to 
(x-50)(x+75) = 0
Positive solution
x = 50 mph is his usual speed
:
:
The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers.
Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000.
 How many total subscribers are needed to bring a total profit of $113,100?
:
Find the present profit: 3000 * $20 = $60000
then: 113100 - 60000 = $53,100 increase in profits
Let n = number of subscribers over 3000 to increase profit by 1 cent for each
.01n = 53100
n = {{{53100/.01}}}
n = 5,310,000 additional subscribers, doesn't seem very realistic, does it!
:
:
Perform the operations and simplify. 
{{{1/x}}} * {{{x^2-15x}}}
------------
 (x - 14)
:
{{{1/x}}} * {{{x(x-15)}}}
------------
 (x - 14)
:
Cancel the x and you are left with
{{{(x-15)/(x-14)}}}