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A certain car averages 25 miles per gallon of gasoline when driven in

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A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post Updated on: 14 Oct 2019, 04:55
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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

Originally posted by leafsrule99 on 11 Aug 2010, 14:17.
Last edited by Bunuel on 14 Oct 2019, 04:55, edited 2 times in total.
Edited the question and added the OA
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 25 Feb 2012, 22:57
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enigma123 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

Struggling on this one too. Any idea how to solve?


Car averages x miles per gallon, means that 1 gallon is enough to drive x miles.

We are asked to find average miles per gallon (miles/gallon) --> average miles per gallon would be total miles driven divided by total gallons used (miles/gallon).

Total miles driven is 10+50=60.

As car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons;
As car averages 40 miles per gallon on the highway for 50 miles on the highway it will use 50/40=1.25 gallons;

So average miles per gallon equals to \(\frac{10+50}{0.4+1.25}\approx{36}\)

Answer: D.
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 22 Aug 2010, 19:49
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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.
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 25 Feb 2012, 21:55
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Hi !

You need average miles/ gallon with the given data

Total Miles traveled => 10+50 = 60

City Fuel Consumption => 1 gallon - 25 miles => 10 Miles - 10/25 gallons => 0.4 gallons
Highway Fuel Consumption => 1 gallon - 40 miles => 50 Miles - 50/40 gallons => 1.25 gallons

Now the tricky part which even I got wrong in my first timed attempt

Average fuel consumption (City + Highway) = 60 miles / (0.4+1.25) = 60/1.65 = 36.6 miles / gallon

divide 60 / 15 = 40 but since 1.65 is greater than 15 the fraction has to be smaller to its either 38 / 36

38 is just too close so eliminate

Hope this helps
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 07 Apr 2012, 02:39
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My take on this -

whenever I see this type of question, I make sure what the question is asking me to solve...and this makes the question easier to solve-

Here, its asking - Total distance travelled/ number of gallons used.-----------------(1)

Now start calculating individual entity.

Total distance = 50+10 = 60

Total galoons - This is the tricky part.

Generally, I solve by using unitary method.

such as - 25 miles ---- 1 gallon
1 mile = 1/25
10 miles = 1/25*10

Similarly calculate for Highway.

Try solving for highway and put the values in equation 1. You will get the answer.

Thanks
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 26 Apr 2012, 17:51
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??
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 26 Apr 2012, 23:09
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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??


Actually we are asked to find the average, but the average of miles per gallon (miles/gallon). So, you should have total miles driven in numerator and total gallons used in denominator (miles/gallon). Now, ask yourself: what do you have in numerator and denominator?
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 27 Apr 2012, 06:34
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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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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 07 Jun 2013, 23:46
Bunnel can you comment on this

Total gallons consumed = 25*10 + 40*50 = 2250
Total miles driven = 50

Avg Mileage in MPG = 2250/50 = 37.5 .. hence close to 38. I picked E pls help me understand
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 08 Jun 2013, 04:12
kapilhede17 wrote:
Bunnel can you comment on this

Total gallons consumed = 25*10 + 40*50 = 2250
Total miles driven = 50

Avg Mileage in MPG = 2250/50 = 37.5 .. hence close to 38. I picked E pls help me understand


Total miles driven is 10+50=60, not 50.
Total gallons used is 0.4+1.25=1.65, not 2250 (!!!). How, could we need 2250 gallons for only 60 miles?

The average miles per gallon (miles/gallons) equals 60/1.65=~36.

Complete solution here: a-certain-car-averages-25-miles-per-gallon-when-driving-in-98942.html#p762784

Hope it's clear.
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 28 Aug 2013, 01:36
I just went through this thread and I have a doubt. Applying Karishma's method of using units, in this case, we get
(25*10+40*50)/(10+ 50) . The units are (miles/g * miles)/ miles = miles/gallon. Please point out the mistake in my logic.
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 28 Aug 2013, 04:07
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pjagadish27 wrote:
I just went through this thread and I have a doubt. Applying Karishma's method of using units, in this case, we get
(25*10+40*50)/(10+ 50) . The units are (miles/g * miles)/ miles = miles/gallon. Please point out the mistake in my logic.


We need total miles in the numerator and gallons in the denominator.

(C1*W1 + C2*W2) should make "miles".
(W1 + W2) should make "gallons".
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 05 Feb 2015, 21:30
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Quote:
A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving 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

I do not understand why weighted average method fails here.



Methods don't fail. You might need to manipulate them in particular circumstances.
You need to understand that whatever is given cannot be the weight. For example, when trying to find the average profit, the weight must be cost price, not number of items or selling price. Similarly, when calculating average speed, weight must be time, not distance. In the same way, here the weight must be amount of fuel used, not distance traveled.
How do you figure out what the weight will be in each case? The units help you in figuring that out.

Check: http://www.veritasprep.com/blog/2014/12 ... -averages/
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 29 May 2017, 03:22
leafsrule99 wrote:
A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving 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

1. Since mileage is varying according to city or highway, average is calculated by total miles traveled / total gallons used
2. Total miles traveled=60
3. total gallons used = gallons used in city + gallons used in highway= 10/25 + 50/40= 33/20
4. So average is 60/(33/20)=36(approx)
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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New post 23 Apr 2019, 20:07
enigma123 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


We can use the formula:

average = total distance/total gallons

average = 60/(10/25 + 50/40)

average = 60/(2/5 + 5/4)

average = 60/(8/20 + 25/20)

average = 60/(33/20)

average = 1200/33 ≈ 36

Answer: D
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Re: A certain car averages 25 miles per gallon of gasoline when driven in  [#permalink]

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