Enterprise rent a car company charges a 45 dollar rental fee, 10 dollars for gas and 0.25 dollars per mile driven. For the same car, Hertz Rent a Car charges $60 for rental and gas, and $0.35 per mile

Question

1) Find the number of miles for which the company's cost will be the same.

2) How much would it cost?

Answer 1

Hi,

It seems like there either might be some missing information (perhaps about gas mileage?) or it's a trick question!

So let's make a formula for Enterprise's Rate: 45$ Rental + 10$ Gas + 0.25$/mile.

We can say that Enterprise's Cost = 55$ + 0.25$ * X, where X is the number of miles traveled.

Hertz's Rate is based on: 60$ for Rental/Gas + 0.35$/mile

So we can say that Hertz's Cost = 60$ + 0.35$ * X, where X is the number of miles traveled.

So if we compare the two cost equations:

Enterprise's Cost = 55$ + 0.25$ * X

Hertz's Cost = 60$ + 0.35$ * X

As you can see, Hertz's starting cost is higher (at X=0) and then increases at a faster rate (35 cents/mile as opposed to 25 cents/mile). Thus, based on the information given, Hertz's Cost is always greater than Enterprise's.

Answer 2

45+10+0.25x = 60+0.35x, solve for x.

55+0.25x = 60+0.35x

0=5+0.1x

-5=0.1x

x=-50

Since x is less than 0, there is no amount that would cause both companies to charge equal amounts.

From a logical point of view, Enterprise charges less money up front and less money per mile compared to Hertz. Therefore Enterprise is cheaper no matter how many miles you drive, so there is no amount of miles driven to cause both companies to charge the same amount.