SOLUTION: Two gasoline distributors, A and B, are 367 km apart on a highway.A charges $1.80/L and B charges $1.68/L. Each charges 0.16¢/L per kilometre for delivery. Where on Interstate 80 i

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Two gasoline distributors, A and B, are 367 km apart on a highway.A charges $1.80/L and B charges $1.68/L. Each charges 0.16¢/L per kilometre for delivery. Where on Interstate 80 i      Log On

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Question 576189: Two gasoline distributors, A and B, are 367 km apart on a highway.A charges $1.80/L and B charges $1.68/L. Each charges 0.16¢/L per kilometre for delivery. Where on Interstate 80 is the cost to the customer the same?
Sir,
I didn't get what is meant by "Interstate 80 is the cost to the customer the same".Even then I tried to solve as follows.
(1.80*0.16)*x=80
(1.68*0.16)*y=80
giving x=277.77 and y=297
I think I have messed it up and cant find the solution.It will be kind of you if you you can help me out in this regards.


Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Read the question a little differently. As in, " 'Where on Interstate 80' is the cost to the customer the same?" Interstate 80 is the name of a highway; I don't know how you put 80 into your equation.

It doesn't say how many gallons you buy, so assume you intend to buy L liters. Suppose you are x kilometers from station A. Then you are 367-A kilometers from station B.

A will charge



B will charge

.

Note the .16Lx is because it is 16 cents *per liter* *per kilometer*.

These two are equal:



The L's cancel. The nice thing about this is that which station is cheaper does not depend on how many liters you buy.



You can solve for x. You should get x = 183.125 (this is 183.125 km from station A), and this is almost exactly halfway between A and B.