Problem Solving

A certain car averages 25 miles per gallon of gasolin when driven in the city and 40 miles per gallon when driven on the highway. According to these rate, 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?

Answer: 36

Please explain how to solve this problem.

Thank you!

Yi

How many gallons of gas will the car consume driving in the city? How about driving on the highway? Now you know total gallons and total miles, you can calculate average miles per gallon.

The problem asks for the average miles per gallon. You need to divide the total number of miles driven by the total miles per gallon. Total Miles/Total Gallons= Total Miles Per Gallon. You know from the problem that the total miles driven was 10 plus 50=60 miles total.

Now, to get the total miles per gallon, you need to divide the total miles by the total gallons.

First, for the city trip, you know the car was driven 10 miles, getting 25 miles per gallon. Therefore, you need to solve for how many gallons were consumed.

Set it up like this: 10 miles/xgallons =25miles/one gallon. Then, solve for x. To do this, I set up a proportion and cross multiplied. X = .4 gallons.

Then, do the same thing for the highway trip. 50 miles/x gallons=40 miles/1gallon. Again, solve for x. X=1.25

Now you have the amount of gallons driven for each scenario. Plug in to the Total equation==> 60/ (.4 +1.25)==> 60/(1.65)=36.36

I hope the rounding is acceptable. Let me know what you think!

Why do we divide by average number of miles per gallon (25+50=75) not by the actual numbers?

Although i really dont know the authenticity of the question as it requires an assumption. the answer will come close to 36. Is it a Gmat question?

I also encountered this problem on my GMAC practice test today. In fact, it was my last question and I was soo pressed for time that I had to guess without even reading it - not suprisingly I got it wrong.

However, in my post exam review I decided to tackle the question before scouting out an answer and came up with the following approach.


City = 25m/gallon x 10m = 250
Highway = 40m/gallon x 50m = 2000
City + Highway / Total Actual Miles = (250 + 2000) / (10 + 50) = 2250 / 60 = 35 5/6

Therefore, the answer is closest to 36.
Effectively, I used a weighted average - although it's a little different to the technique shown above. Is this ok?

Total Miles Driven: 10+50 = 60
Highway mpg: Drove 50 miles at rate of 40mpg, so consumed 1 10/40 = 1 1/4 = 5/4 gallons
City mpg: Drove 10 miles at rate of 25 mpg, so consumed 10/25 = 2/5 gallons

5/4+2/5= 25/20+8/20 = 33/20

60/33/20 = 1200/33 = About 36

tgou008 wrote:I also encountered this problem on my GMAC practice test today. In fact, it was my last question and I was soo pressed for time that I had to guess without even reading it - not suprisingly I got it wrong.

However, in my post exam review I decided to tackle the question before scouting out an answer and came up with the following approach.


City = 25m/gallon x 10m = 250
Highway = 40m/gallon x 50m = 2000
City + Highway / Total Actual Miles = (250 + 2000) / (10 + 50) = 2250 / 60 = 35 5/6

Therefore, the answer is closest to 36.
Effectively, I used a weighted average - although it's a little different to the technique shown above. Is this ok?

2250/60 is 37.5, not 35 5/6

yichunette wrote:A certain car averages 25 miles per gallon of gasolin when driven in the city and 40 miles per gallon when driven on the highway. According to these rate, 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?

Answer: 36

Please explain how to solve this problem.

Thank you!

Yi

Per means division. Miles per gallon means miles/gallons.

City miles:Highway miles = 10:50 = 1:5.
Any values that conform to this ratio will yield the same average miles per gallon.

To make the math easy, plug in numbers that are multiples of 25 and 40.
Let city miles = 200 and highway miles = 1000. (200:1000 = 1:5.)
Gas used in the city = 200/25 = 8.
Gas used on the highway = 1000/40 = 25.
Total gas used = 8+25 = 33.
Total Miles/Total Gas = 1200/33 = 400/11 ≈ 36.

Can anyone explain why you have to convert to gallons instead of using weighted average. I used the weighted average method and it provides an answer of 37.5...

(1/6) (25) + (5/6) (40) = 37.5

Hi,

Sorry I didn't understand this question. Can someone please elaborate on the answer? Thanks!

Average speed = Total distance/Total time

Total distance here = 10+50 = 60
Total time = 10/25+50/40

Avg Speed=60/330/200 = 60*200/330 = 36.3mph