Question

Ravi drove 260 miles using 12 gallons of gas. At this rate, how many gallons of gas would he need to drive 286 miles?

Answer 1

Explanations:

Let the distance traveled by Ravi be "d"

Let the number of gallons used to be "g"

The relationship between the distance traveled and the number of gallons is a direct proportionality. Mathematically;

`\begin{gathered} \text{ d }\propto\text{ g} \\ \text{ d = kg} \\ \text{ k = }(d)/(g) \end{gathered}`

k is the variation constant

If Ravi drove 260 miles using 12 gallons of gas, this means that

d = 260 miles and g = 12 gallons. Substitute the given values into the formula;

`\begin{gathered} k=(260)/(12) \\ k=(65)/(3) \end{gathered}`

To calculate the number of gallons of gas he would need to drive 286 miles, substitute k = 65/3 and d = 286miles into the original formula.

`\begin{gathered} d=kg \\ 286=(65)/(3)g \\ 65g=286*3 \\ g=(286*3)/(65) \\ g=(858)/(65) \\ g=13.2gallons \end{gathered}`

Hence the number of gallons needed to drive 286 miles is 13.2gallons