SOLUTION: Please help me solve this problem: A trip of 189 miles can take one hour less if gerald increases the average speed of his car by 12 miles per hour. What was the original average s

Question 963050: Please help me solve this problem: A trip of 189 miles can take one hour less if gerald increases the average speed of his car by 12 miles per hour. What was the original average speed of the car?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A trip of 189 miles can take one hour less if gerald increases the average speed of his car by 12 miles per hour.
What was the original average speed of the car?
:
let s = the original speed
then
(s+12) = the increased speed
:
Write a time equation, time = dist/speed
:
Original time - faster time = 1 hr
- = 1
multiply equation by s(s+12), cancel the denominators and you have
189(s+12) - 189s = s(s+12)
189s + 2268 - 189s = s^2 + 12s
Combine to form a quadratic equation on the right
0 = s^2 + 12s - 2268
you can use the quadratic formula; a=1; b=12; c=-2268
But this will factor to
(s+54)(s-42) = 0
the positive solution is what we want here\
s = 42 mph is the original speed
:
:
Check this by finding the actual time at each speed.
189/42 = 4.5 hrs
189/54 = 3.5 hrs, 1 hr less
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