SOLUTION: This word problem is giving me headaches: Two gas distributors, A and B are 228mi apart on Interstate 80. A charges $0.85 per gallon and B charges $0.80 per gallon. Each charges $

Question 395717: This word problem is giving me headaches:
Two gas distributors, A and B are 228mi apart on Interstate 80. A charges $0.85 per gallon and B charges $0.80 per gallon. Each charges $0.05 per gallon per mile for delivery. Where on Interstate 80 is the cost to the customer the same.
I am having the hardest time with the per gallon per mile part.
Please explain
Thank you so much
lufkin@ureach.com
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two gas distributors, A and B are 228 mi apart on Interstate 80.
A charges $0.85 per gallon and B charges $0.80 per gallon.
Each charges $0.05 per gallon per mile for delivery.
Where on Interstate 80 is the cost to the customer the same.
:
let d = distance from A to the point of equal cost
then
(228-d) = distance from B to the point of equal cost
:
Cost per gal
From A = From B
.85 + .05d = .80 + .05(228-d)
.85 + .05d = .80 + 11.4 - .05d
.85 + .05d = 12.2 - .05d
.05d + .05d = .12.2 - .85
.10d = 11.35
d =
d = 113.5 mi from A, cost will be the same
:
:
Check this by finding the actual cost
A: 113.5(.05) + .85 = $6.525 per gal
B: (228-113.5)(.05) + .80 = $6.525; confirms our solution of 113.5 mi from A
:
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