Question 395717
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 = {{{11.35/.1}}}
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

:
Did this make sense you?