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 ½ hour longer than Bob’s. Find the s
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Question 211759: 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 ½ hour longer than Bob’s. Find the speed at which each of them is 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 ½ hour longer than Bob’s.
Find the speed at which each of them is 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 hour - = .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
.5s^2 + 2.5s + 5s - 350 = 0
:
.5s^2 + 7.5s - 350 = 0
:
Multiply by 2, get rid of the decimals
s^2 + 15s - 700 = 0
Factor
(s+35)(s-20) = 0
:
positive solution
s = 20 mph is Pat's speed
and
20 + 5 = 25 mph is Bob's speed
;
:
Check solutions, find the times of each
70/20 = 3.5 hr
75/25 = 3.0
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diff: = .5 hrs
