Step 1 :David is considering renting a truck for one day from either Company A or Company B. Company A charges a flat rate of $79 with unlimited mileage, while Company B charges an initial fee of $65 and an additional $0.70 for every mile driven.
Step 2 :We need to find the number of miles for which the cost of renting from company A is less than the cost of renting from company B. This can be represented by the inequality \(79 < 65 + 0.7m\), where \(m\) represents the number of miles driven.
Step 3 :Solving the inequality for \(m\), we get \(m > 20.0\).
Step 4 :This means that for any mileage greater than 20 miles, company A will charge less than company B. Therefore, David should choose company A if he plans to drive more than 20 miles.
Step 5 :\(\boxed{m > 20}\) is the final answer. For mileages greater than 20 miles, company A will charge less than company B.