Question

the function $y = \frac{60}{x}$ relates $y$, the time in hours that it takes michael to travel to his grandparents house, to $x$, his average speed in miles per hour. what does the number 60 in the function represent?
the time, in hours, that it takes to get to michaels grandparents house
the fuel, in gallons, that is used to get to michaels grandparents house
the distance, in miles, that must be traveled to get to michaels grandparents house
the rate, in miles per hour, that michael travels to get to his grandparents house

Explanation:

Step1: Recall the distance formula

The formula relating distance (\(d\)), speed (\(x\)), and time (\(y\)) is \(d = x\times y\), which can be rearranged as \(y=\frac{d}{x}\).

Step2: Compare with the given function

The given function is \(y = \frac{60}{x}\). Comparing with \(y=\frac{d}{x}\), we can see that \(d = 60\). Since \(x\) is the average speed in miles per hour and \(y\) is the time in hours, \(d\) (which is 60 here) represents the distance in miles.

Now let's analyze the options:

• Option 1: "the time, in hours, that it takes to get to Michael’s grandparents’ house" is \(y\), not 60. Eliminate.
• Option 2: "the fuel, in gallons, that is used to get to Michael’s grandparents’ house" – the function is about speed, time, and distance, not fuel. Eliminate.
• Option 3: "the distance, in miles, that must be traveled to get to Michael’s grandparents’ house" – matches our analysis as 60 is the distance.
• Option 4: "the rate, in miles per hour, that Michael travels to get to his grandparents’ house" is \(x\), not 60. Eliminate.

Answer:

the distance, in miles, that must be traveled to get to Michael’s grandparents’ house