This is identical to a question which asks for average speed. To find the answer we will use theequation: (Total Distance)/(Total Gallons Used) =28
TotalDistance: We are told that the car drives 120 miles in the city and 300 on thehighway. \( 120+300 =420\)
Total GallonsUsed: We know that in the city the car drives x miles per gallon. Therefore the total gallons of fuel used in the city willbe \(\frac{120}{x}\)
We know on the highway that the car drives 2x miles per gallon. Therefore the total gallons of fuel used on the highway willbe \(\frac{300}{2x}\)
Putting Together and Solving forx:
\(\frac{420}{\frac{120}{x}+\frac{300}{2x}}=28\)
\(\frac{420}{\frac{540}{2x}}=28\)
\( 420 *\frac{2x}{540} =28\)
\( x =18\)
ANSWERC
Alternativemethod:
One could use alligation and the answer choices to very quickly find the answer:
One is essentially 'mixing'\(x\) and\(2x\) in a ratioof \(120:300\) (which simplifiesto \(2:5\) ) to get28.
\(x\) \(2x\)
\(28\)
\(2\) [m]
...
TotalDistance: We are told that the car drives 120 miles in the city and 300 on thehighway. \( 120+300 =420\)
Total GallonsUsed: We know that in the city the car drives x miles per gallon. Therefore the total gallons of fuel used in the city willbe \(\frac{120}{x}\)
We know on the highway that the car drives 2x miles per gallon. Therefore the total gallons of fuel used on the highway willbe \(\frac{300}{2x}\)
Putting Together and Solving forx:
\(\frac{420}{\frac{120}{x}+\frac{300}{2x}}=28\)
\(\frac{420}{\frac{540}{2x}}=28\)
\( 420 *\frac{2x}{540} =28\)
\( x =18\)
ANSWERC
Alternativemethod:
One could use alligation and the answer choices to very quickly find the answer:
One is essentially 'mixing'\(x\) and\(2x\) in a ratioof \(120:300\) (which simplifiesto \(2:5\) ) to get28.
\(x\) \(2x\)
\(28\)
\(2\) [m]
...
Statistics : Posted by Nidzo • on 05 Jul 2024, 01:30 • Replies 2 • Views 113
