SOLUTION: Lisa drove 100 miles, then increased her speed by 25 miles per hour for 225 miles. If the second part of the drive took 1 hour longer than the first part, find her average speed.

Question 592150: Lisa drove 100 miles, then increased her speed by 25 miles per hour for 225 miles. If the second part of the drive took 1 hour longer than the first part, find her average speed.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
drove 100 miles, then increased her speed by 25 miles per hour for 225 miles.
If the second part of the drive took 1 hour longer than the first part, find her average speed.
:
Let s = speed the 1s 100 miles
then
(s+25) = speed on the last 225 miles
:
Write a time equation; time = dist/speed
- = 1
multiply by s(s+25)
s(s+25)* - s(s+25)* = s(s+25)
225s - 100(s+25) = s^2 + 25s
225s - 100s - 2500 = s^2 + 25s
125s - 2500 = s^2 + 25s
0 = s^2 + 25s - 125s + 2500
A quadratic equation
s^2 - 100s + 2500 = 0
Factors to:
(s-50)(s-50) = 0
s = 50 mph on the 1st 100 mi
then
75 mph on last 225 mi
:
Let a = average speed for the whole trip which was 325 mi
+ =
multiply by 150a to clear the denominators; results
3a(100) + 2a(225) = 150(325)
300a + 450a = 48750
750a = 48750
a = 65 mph is the average speed for the trip
:
:
Check this out with a time equation
100/50 + 225/75 = 325/65
2 + 3 = 5
RELATED QUESTIONS
Lisa drove 60 miles, then increased her speed by 15 miles per hour for 135 miles. If the... (answered by josmiceli)

Lisa drove 180 miles, then increased her speed by 15 miles per hour for 405 miles. If the (answered by josmiceli)

1)Lisa drove 60 miles, then increased her speed by 15 miles per hour for 135 miles. If... (answered by jorel1380,MathTherapy)

Lisa drove 60 miles on a highway, then increased her speed by 20 miles per hour for 240... (answered by josgarithmetic)

Suppose Liz drove 100 miles then increased her speed by 30mph for the following 200... (answered by richwmiller)

On a road trip Maura drove at a speed of 60 miles per hour for the first 2 hours she then (answered by josmiceli)

A woman drives 10 miles, then increases her speed by 10 miles per hour and drives 25... (answered by fractalier)

Angela drove 100 miles to Batonsville at an average speed of 50 miles per hour. She then... (answered by ankor@dixie-net.com)

a jogger ran 3 miles, decrease her speed by 1 mile per hour, and then ran another 4... (answered by lwsshak3)