average speed

[akesh]

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?

Choices -
28
30
33
36
38

Thanks for your help!

[venkhatapriya]

Avg miles per gallon = Total distance traveled / Total gallons used

Total distance traveled = 50 miles

Total gallons used = 10/25 + 50/40 = 33/20 ~= 30/20

Therefore, Avg miles per gallon = ( 50 * 20 ) / 30 = 100 / 3 = 33.33 ~= 33

[akesh]

thank you.

But isn't the total miles traveled = 10 + 50 = 60 ?

[venkhatapriya]

Lol i missed it !! Then it is = 60 * 20 / 33 = 36.3 ~= 36 !!
Sorry !! [:P]

[cyber_office]

Should it be 37.5?

(10/60) * 25 + (50/60) * 40 = 37.5

Can you post the OA?

Thanks.

[akesh]

I too was getting 37.5.

But the correct answer choice was 36. Didn't make sense to me.

[cyber_office]

Hi,

I think Priya's solution is definitely correct. (Total distance)/(Total gallons) will yield average MPG. However, what I find vexing is that the weighted average approach we used does not result in the same answer. We must be missing some key element of the underlying logic here. Hopefully, it won't remain elusive for too long.

Regards.

[saurabhbhardwaj]

can someone please explain how the following (total) is calculated?

Total gallons used = 10/25 + 50/40 = 33/20 ~= 30/20

Might sound like a silly question, but please help.

[yelena_av]

Hi,

I think Priya's solution is definitely correct. (Total distance)/(Total gallons) will yield average MPG. However, what I find vexing is that the weighted average approach we used does not result in the same answer. We must be missing some key element of the underlying logic here. Hopefully, it won't remain elusive for too long.

Regards.

The weights should be gallons and not miles...

10/25=0.4 gallons were used to drive 25 miles

50/40=1.25 gallons were used to drive 50 miles

Total gallons = 0.4+1.25=1.65

Weighting by gallons (not miles),
25*0.4/1.65+40*1.25/1.65=36.36

[cyber_office]

I agree. But I thought the weighted average could also be calculated as follows:

1/6 of the journey * MPG (i.e., 25 mpg) + 5/6 of the journey * MPG (i.e., 40 mpg)

It should result in the same answer unless I am still missing something.

To the prior-to-previous poster:

How is this calculated - Total gallons used = 10/25 + 50/40 = 33/20 ~= 30/20

It's direct proportion:

25 miles - from 1 gallon
10 miles - How many gallons?

Use direct proportion and invert and get 10/25.

[yelena_av]

I agree. But I thought the weighted average could also be calculated as follows:

1/6 of the journey * MPG (i.e., 25 mpg) + 5/6 of the journey * MPG (i.e., 40 mpg)

It should result in the same answer unless I am still missing something.

.

The weighted average will work only if you use the right weights. If you use the wrong weights (like miles in this case), obviously it will lead to a completely different result...

Think about the more common speed problem which can lead to the same confusion...if you have a car that drives 120 miles, half way at a speed 10 km/hour and half way at a speed 20 km/hour, the average seed for the entire trip is NOT 10/2+20/2=15. The average speed will be calculated total distance/total time=120/9=13.333...the first 60 miles the car drives in 6 hours at the average speed of 10, the remaining 60 miles the car drives in 3 hours at the average speed 20. Using miles as weights was wrong and resulted in the wrong answer. Now using the HOURS as weights, the weighted average gives the same reult: 10*6/9+20*3/9=120/9=13.333...

[cyber_office]

Thanks...got it!

[RonPurewal]

already a long post here:
a-certain-car-averages-25-miles-per-gallon-t3383.html