Thomas is headed to his grandmother’s house. he travels on the interstate for 1.5 hours at a speed of 70 miles per hour. his car gets 35 miles to the gallon. how many gallons will he use on the trip?

Thomas will use 3 gallons on the trip.

Step-by-step explanation:

This can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

To know how many gallons Thomas will use on the trip, the first step is to know how many miles he traveled.

So our measures are:

- The speed in miles per hour

- The distance traveled in miles

As one of these measures increases, so will the other, so the relationship is direct.

We know that he travels at a speed of 70 miles per hour, for 1.5 miles, so:

1 hour - 70 miles

1.5 hours - x miles

x = 70*1.5 = 105 miles.

So Thomas travels 105 miles, and we want to know how many gallons will he use. We know that the car gets 35 milles a gallon, so:

1 gallon - 35 miles

x gallons - 105 miles

35x = 105

x = 3.

So, Thomas will use 3 gallons on the trip.

A step function

Step-by-step explanation:

In a step function, the y-value remains constant for several values of x.  The y-value then "steps" up for the next category with the next several values of x.

In this function, the y-value will be 3.5 for the x-values from 0 to 25.

The function then "steps" up to a y-value of 5.95 for the x values from 25.01 to 75.

The next "step" goes to a y-value of 7.95 for x-values from 75.01 to 125.

The last "step" goes to a y-value of 9.95 for x-values of 125.01 and up.