A restaurant's delivery person can determine the number of miles he can drive in $x$ hours by the function $f(x) = 22x$. The number of gallons of gas the delivery person uses driving $y$ miles can be determined by the function $g(y) = \frac{y}{22}$. If the delivery person works an 8-hour shift, how many gallons of gas does he use?
Answer (2)
Calculate the total miles driven in 8 hours: f ( 8 ) = 22 × 8 = 176 miles.
Calculate the amount of gasoline needed for 176 miles: g ( 176 ) = 22 176 = 8 gallons.
The delivery person needs 8 gallons of gasoline for the 8-hour shift.
The final answer is 8 .
Explanation
Understanding the Problem Let's analyze the problem. We are given two functions: f ( x ) = 22 x , which tells us how many miles the delivery person can drive in x hours, and g ( y ) = 22 y , which tells us how many gallons of gasoline are required to drive y miles. We are also told that the delivery person works an 8-hour shift. Our goal is to find out how many gallons of gasoline the delivery person needs for the 8-hour shift.
Calculate Miles Driven First, we need to find the number of miles the delivery person can drive in 8 hours. We can use the function f ( x ) for this, where x is the number of hours. In this case, x = 8 . So we have: f ( 8 ) = 22 × 8 = 176 This means the delivery person can drive 176 miles in 8 hours.
Calculate Gasoline Needed Next, we need to find out how many gallons of gasoline are required to drive 176 miles. We can use the function g ( y ) for this, where y is the number of miles. In this case, y = 176 . So we have: g ( 176 ) = 22 176 = 8 This means the delivery person needs 8 gallons of gasoline for the 8-hour shift.
Final Answer Therefore, the delivery person needs 8 gallons of gasoline for an 8-hour shift.
Examples
This type of problem can be used in logistics and transportation to estimate fuel consumption for delivery routes. For example, a delivery company might use similar functions to plan routes and allocate fuel resources for their drivers. By knowing the relationship between driving time, distance, and fuel consumption, the company can optimize its operations and reduce costs. If a company knows that a driver works 10 hours and the function is f ( x ) = 30 x and g ( y ) = 25 y , then the company can calculate the amount of gasoline needed as follows: f ( 10 ) = 30 × 10 = 300 miles, and g ( 300 ) = 25 300 = 12 gallons.
The delivery person drives 176 miles in an 8-hour shift, which requires 8 gallons of gasoline. This is calculated using the functions provided: f ( x ) = 22 x for distance and g ( y ) = 22 y for gasoline consumption. Thus, the final answer is 8 gallons of gas used.
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