khushboochhabra wrote:
I got Bunuel's approach.. but was wondering if weighed average should work here that is
(1*25+5*40)/6 = 37.5 ~ 38
Seems it doesnt work here.. But shouldn't it??
'Distances traveled' (i.e. ratio of 1:5) cannot be the weights here to find the average mileage. The weights have to be 'number of gallons'.
If we change the question and make it:
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 uses 10 gallons in the city and then 50 gallons on the highway
Now you can use (1*25+5*40)/6
Why?
Whenever you are confused what the weights should be (e.g. here should the weights be the distance traveled or should they be gallons of fuel used...), look at the units.
Average required is \(\frac{miles}{gallon}\). So you are trying to find the weighted average of two quantities whose units must be \(\frac{miles}{gallon}\).
\(C_{avg} = \frac{C_1*W_1 + C_2*W_2}{{W_1 + W_2}}\)
\(C_{avg}, C_1, C_2 - \frac{miles}{gallon}\)
So \(W_1\) and \(W_2\) should be in gallon to get:
\(\frac{miles}{gallon} = (\frac{miles}{gallon}*gallon + \frac{miles}{gallon}*gallon)/(gallon + gallon)\)
Only if weights are in gallons, do we get 'Total miles' in the numerator and 'Total gallons' in the denominator.
We know that Average miles/gallon = Total miles/Total gallons
[highlight]Takeaway: The weights have to be the denominator units of the average.[/highlight]
So what do we do in this question?
What is the distance travelled (i.e.total miles)?
(10+50) = 60
What is the total gallons used?
Fuel used in the city = 10/25
Fuel used to go from B to C = 50/40
So Average miles/gallon = (60)/(10/25 + 50/40) = apprx 36
You need to know what the weights are going to be. Here, weights have to be the amount of fuel used i.e. in gallons because you are looking for average miles per gallon.
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