A restaurant's delivery person can determine the number of miles he can drive in $x$ hours by the driving $y$ miles can be determined by the function [tex]g(y)=\frac{y}{22}[/tex]. If the delivery person works an 8-hour shift, what is the maximum number of miles he can drive?

Question

GinnyAnswer · Answer

The problem provides a function g ( y ) = 22 y ​ that determines the number of hours it takes to drive y miles. 
 We set up the equation 22 y ​ = 8 to find the number of miles the delivery person can drive in 8 hours. 
 We solve for y by multiplying both sides of the equation by 22. 
 The delivery person can drive 176 ​ miles in an 8-hour workday. 
 
 Explanation 
 
 Understanding the Problem The problem states that the function g ( y ) = 22 y ​ determines the number of hours it takes to drive y miles. The delivery person works 8 hours a day. We need to determine the number of miles the delivery person can drive in an 8-hour workday. 
 
 Setting up the Equation Since g ( y ) gives the time it takes to drive y miles, we want to find the value of y such that g ( y ) = 8 . In other words, we want to solve the equation 22 y ​ = 8 for y . 
 
 Solving for y To solve for y , we multiply both sides of the equation by 22: y = 8 × 22 
 
 Finding the Answer Multiplying 8 by 22, we get: y = 176 Therefore, the delivery person can drive 176 miles in an 8-hour workday.

Examples 
 Understanding how distance, rate, and time relate is crucial in logistics and transportation. For example, a delivery company needs to optimize routes for its drivers to minimize delivery times and fuel costs. By knowing the average speed of their vehicles and the time available for deliveries, they can calculate the maximum distance a driver can cover in a day. This helps in planning efficient delivery schedules and ensuring timely service to customers.

Anonymous · Answer

The maximum number of miles the delivery person can drive in an 8-hour shift is 176 miles, calculated by solving the equation derived from the function given. This is done by substituting the hours into the function and multiplying accordingly. Thus, the delivery person can efficiently maximize their driving distance based on the hours worked. 
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A restaurant's delivery person can determine the number of miles he can drive in $x$ hours by the driving $y$ miles can be determined by the function [tex]g(y)=\frac{y}{22}[/tex]. If the delivery person works an 8-hour shift, what is the maximum number of miles he can drive?

Answer (2)

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