Question

Tony used a total of 5 1/6 gallons of gas while driving his car. Each hour he was driving, he used 5/9 gallons of gas. What was the total number of hours he was driving?

Answer 1

We know the total number of gallons of gas used: 5 1/6

We know the number of gallons used per hour: 5/9

The total number of gallons used is equal to the number of gallons used per hour times the number of hours

gallons = gallons per hour * hours

Substitute the information we are given

5 1/6 = 5/9 * h

We use the variable h since we do not know the hours.

Divide each side by 5/9 to isolate the number of hours.

`\frac{5\text{ 1/6}}{(5)/(9)}=\text{ h}`

Now we need to change the mixed number to a improper fraction.

Take the denominator and multiply by the whole number then add the numerator

6*5 +1 = 30 +1 = 31

Then divide by the denominator

`((31)/(6))/((5)/(9))=h`

Now use copy dot flip to change this to multiplication.

`(31)/(6)\cdot\text{ }(9)/(5)\text{ = h}`
`(31)/(2)\cdot(3)/(5)=h`

We found this by dividing ther 9 and the 6 by 3

This gives us 93/10 for h

But this is an improper fraction. Changing this to a mixed number

93/10 = 9 3/10 hours