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.
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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
