Chaithraln2499 wrote:
Is this a weighted average question?
GeminiHeat wrote:
A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
(A) 28
(B) 30
(C) 33
(D) 36
(E) 38
Average miles per gallon is given by: Total distance traveled/Total gallons used.
Total distance traveled is given to us and is equal to 10+50 = 60 miles
Total gallons used can be determined by reverse working the formula listed above.
Number of gallons in the city = Total distance / Average = \(\frac{10}{25}\)
Number of gallons in the highway = Total distance / Average = \(\frac{50}{40}\)
Total number of gallons = Sum of the above two quantities.
So the average overall
\(\frac{60}{\frac{10}{25} + \frac{5}{4}} = \frac{60}{\frac{2}{5} + \frac{5}{4}} =
\frac{60}{\frac{33}{20}} = \frac{1200}{33} = \frac{400}{11}\)
If you solve this you get 36.3636. So the answer is 36.