Zachary can spend no more than $\mathrm{\$}67$
per day to rent a car. A car rents for $\mathrm{\$}40$ per day plus $\mathrm{\$}0.18$ per mile. What is the maximum number of miles that he can drive the car?

Step 1 ：Zachary can spend no more than $67perdaytorentacar.Acarrentsfor$40 per day plus $0.18 per mile. We need to find out the maximum number of miles that he can drive the car.

Step 2 ：First, we calculate how much money Zachary has left after paying the daily rental fee. This is done by subtracting the daily rental fee from his maximum daily budget. The result is the amount of money he has left to spend on mileage. $67-40=27$

Step 3 ：To find out how many miles he can drive, we divide this amount by the cost per mile. $\frac{27}{0.18}=150$

Step 4 ：Final Answer: The maximum number of miles that Zachary can drive the car is $\boxed{{\displaystyle 150}}$.