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
Algebra.Com
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) (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 =
:
Pat's time - Bob's time = one-half hr
- = .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
RELATED QUESTIONS
Pat travels 70 miles on her milk route and Bob travels 75 miles on his route. Pat travels (answered by Nate)
Pat travels 70 miles on her milk route and Bob travels 75 miles on his route. Pat travels (answered by ankor@dixie-net.com)
Pat travels 70 miles on her milk route, and Bob travels 75 miles on his route. Pat... (answered by dkppathak)
Pat travels 70 miles on her milk route, and Bob travels 75 miles on his route. Pattravels (answered by stanbon)
A small company involved in a delivery business is in charge of two routes. A driver on... (answered by checkley71)
Two cars are traveling on two different routes, one 43 miles longer than the other. The... (answered by josmiceli)
On Jeff's outgoing trip, he travels 648 miles and uses 18 gallons of gas. On his return... (answered by Theo)
"Pat leaves home and rides his bicycle out into the country for 2 hours. On this return... (answered by htmentor)
A man travels a distance of 20 miles at 60 miles per hour and then returns over the same... (answered by stanbon)