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QuestionCalculate the miles per gallon if Dave and Mary drove 29014290 \frac{1}{4} miles using 131213 \frac{1}{2} gallons of gas.

Studdy Solution

STEP 1

Assumptions1. The total distance driven is 29014290 \frac{1}{4} miles. The total amount of gas used is 13113 \frac{1}{} gallons3. We are asked to find the miles per gallon, which is the total distance divided by the total gas used

STEP 2

First, we need to convert the mixed numbers to improper fractions to make the calculations easier.For the distance, the conversion is as follows29014=290+14=290×4+14290 \frac{1}{4} =290 + \frac{1}{4} = \frac{290 \times4 +1}{4}

STEP 3

Now, calculate the improper fraction for the distance.
2901=290×+1=1161290 \frac{1}{} = \frac{290 \times +1}{} = \frac{1161}{}

STEP 4

Next, we convert the mixed number for the gas used to an improper fraction. The conversion is as follows1312=13+12=13×2+1213 \frac{1}{2} =13 + \frac{1}{2} = \frac{13 \times2 +1}{2}

STEP 5

Now, calculate the improper fraction for the gas used.
1312=13×2+12=27213 \frac{1}{2} = \frac{13 \times2 +1}{2} = \frac{27}{2}

STEP 6

Now that we have the distance and gas used as improper fractions, we can calculate the miles per gallon by dividing the distance by the gas used.
Miles per gallon=DistanceGas usedMiles\, per\, gallon = \frac{Distance}{Gas\, used}

STEP 7

Plug in the values for the distance and the gas used to calculate the miles per gallon.
Miles per gallon=11614272Miles\, per\, gallon = \frac{\frac{1161}{4}}{\frac{27}{2}}

STEP 8

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Miles per gallon=11614×227Miles\, per\, gallon = \frac{1161}{4} \times \frac{2}{27}

STEP 9

Now, perform the multiplication to calculate the miles per gallon.
Miles per gallon=116×24×27Miles\, per\, gallon = \frac{116 \times2}{4 \times27}

STEP 10

implify the multiplication to get the final answer.
Miles per gallon=2322108≈21.5Miles\, per\, gallon = \frac{2322}{108} \approx21.5Dave and Mary Smith got approximately21.5 miles per gallon in their vehicle.

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