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akesh
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Post subject: average speed  Posted: Mon Dec 07, 2009 12:51 am |
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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?
Choices -
28
30
33
36
38
Thanks for your help!
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venkhatapriya
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Post subject: Re: average speed Posted: Mon Dec 07, 2009 5:14 am |
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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
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akesh
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Post subject: Re: average speed Posted: Mon Dec 07, 2009 11:06 am |
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thank you.
But isn't the total miles traveled = 10 + 50 = 60 ?
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venkhatapriya
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Post subject: Re: average speed Posted: Mon Dec 07, 2009 11:40 am |
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Lol i missed it !! Then it is = 60 * 20 / 33 = 36.3 ~= 36 !!
Sorry !! [:P]
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cyber_office
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Post subject: Re: average speed Posted: Mon Dec 07, 2009 12:26 pm |
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Should it be 37.5?
(10/60) * 25 + (50/60) * 40 = 37.5
Can you post the OA?
Thanks.
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akesh
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Post subject: Re: average speed Posted: Mon Dec 07, 2009 5:30 pm |
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I too was getting 37.5.
But the correct answer choice was 36. Didn't make sense to me.
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cyber_office
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Post subject: Re: average speed Posted: Mon Dec 07, 2009 6:05 pm |
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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.
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saurabhbhardwaj
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Post subject: Re: average speed Posted: Tue Dec 08, 2009 12:48 pm |
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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.
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yelena_av
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Post subject: Re: average speed Posted: Tue Dec 08, 2009 2:26 pm |
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cyber_office wrote: 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
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cyber_office
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Post subject: Re: average speed Posted: Tue Dec 08, 2009 8:48 pm |
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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.
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yelena_av
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Post subject: Re: average speed Posted: Wed Dec 09, 2009 11:40 am |
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cyber_office wrote: 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...
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cyber_office
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Post subject: Re: average speed Posted: Wed Dec 09, 2009 1:31 pm |
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Posts: 38
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RonPurewal
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Post subject: Re: average speed Posted: Sat Jan 09, 2010 4:25 am |
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