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Mathematics

Hareg's motorcycle uses 1 gallon of gas for every 30 miles traveled when traveling at an average speed of 60 miles per hour. The motorcycle's gas tank has 5 gallons at the beginning of a trip. If Hareg's motorcycle travels at an average speed of 60 miles per hour, which of the following functions best models the number of gallons of gas, g(h), remaining in the tank h hours after the trip begins?

A.g(h)=5-2h
B.g(h)=5-h/2
C.g(h)=(5-60h)/30
D.g(h)=(5-30h)/60

答案和解析

答案：A

解析：

Choice A is correct. Since Hareg's motorcycle travels at an average speed of 60 miles per hour and the motorcycle's gas mileage is 30 miles per gallon, the number of gallons of gas used each hour can be represented with:

(60miles/1hour)*(1gallon/30miles)=2gallons per hour

Therefore, the motorcycle uses 2h gallons of gas in h hours.

Since the motorcycle's gas tank has 5 gallons of gas when the trip begins, we can represent the total amount of gas in the tank, g(h), after h hours of driving during which the motorcycle uses 2h gallons of gas per hour can be represented with the following equation g(h)=5-2h.

The function that best models the amount of gas, g(h), in the tank after h hours of driving is g(h)=5-2h.