SOLUTION: Pat travels 70 miles on her milk route, and Bob travels 75 miles on his route. Pat travels 5 miles per hour slower than Bob, and her route takes her one-half hour longer than Bo

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Question 181395: Pat travels 70 miles on her milk route, and
Bob travels 75 miles on his route. Pat travels 5 miles per
hour slower than Bob, and her route takes her one-half hour
longer than Bob’s. How fast is each one traveling?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Pat travels 70 miles on her milk route, and
Bob travels 75 miles on his route. Pat travels 5 miles per
hour slower than Bob, and her route takes her one-half hour
longer than Bob’s. How fast is each one traveling?
:
Let s = Pat's speed
then
(s+5) = Bob's speed
:
Write a time equation: Time = dist%2Ftime
:
Pat's time - Bob's time = one-half hr
70%2Fs - 75%2F%28%28s%2B5%29%29 = .5
Multiply equation by s(s+5); results:
70(s+5) - 75s = .5s(s+5)
:
70s + 350 - 75s = .5s^2 + 2.5s
:
-5s + 350 = .5s^2 + 2.5s
:
Arrange as a quadratic equation
0 = .5s^2 + 2.5s + 5s - 350
:
.5s^2 + 7.5s - 350 = 0
:
Multiply equation by 2 to make the coefficient of s^2 = 1
s^2 + 15s - 700 = 0
:
Factor this to
(s+35)(s-20) = 0
:
We want the positive solution here:
s = 20 mph is Pat's speed
then
25 mph is Bob's speed
:
:
Check the solutions by finding the times
Pat: 70/20 = 3.5 hr
Bob: 75/25 = 3.0
----------------
difference: .5 hrs, confirms our solutions