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Weighted Averages

by kartikshah » Thu Jul 26, 2012 1:24 pm
Here's a question from VeritasPrep that I got wrong:

How many hours does it take Abbas to travel 245 miles if he spends 1/3 of the time at 20 miles an hour, 1/3 of the time at 40 miles an hour and 1/3 of the time at 80 miles an hour.

A-1.75
B-5.25
C-5.5
D-5.75
E-7.14

The solution provided is D=R*T (245 = {(20+40+80)/3} * T
I understood that part.

My question is if the question was modified to read 1/3, 1/6 and 1/12th of the time how would I solve it?
Would I have to then take ratios and proceed?

Thanks!
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by eagleeye » Thu Jul 26, 2012 1:36 pm
kartikshah wrote:Here's a question from VeritasPrep that I got wrong:

How many hours does it take Abbas to travel 245 miles if he spends 1/3 of the time at 20 miles an hour, 1/3 of the time at 40 miles an hour and 1/3 of the time at 80 miles an hour.

A-1.75
B-5.25
C-5.5
D-5.75
E-7.14

The solution provided is D=R*T (245 = {(20+40+80)/3} * T
I understood that part.

My question is if the question was modified to read 1/3, 1/6 and 1/12th of the time how would I solve it?
Would I have to then take ratios and proceed?

Thanks!
You would not be able to solve 1/3, 1/6 and 1/12 because it doesn't add upto 1.

However if the question said, 2/3 @ 20, 1/4 @ 40, 1/12 @80 (say), then solve:

245 = T * (2/3*20 + 1/4*40 + 1/12*80).

Let me know if this helps :)
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by kartikshah » Thu Jul 26, 2012 1:38 pm
Yes, that's true! It does not add up to 1!
Thanks!
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by GMATGuruNY » Fri Jul 27, 2012 2:38 am
kartikshah wrote:Here's a question from VeritasPrep that I got wrong:

How many hours does it take Abbas to travel 245 miles if he spends 1/3 of the time at 20 miles an hour, 1/3 of the time at 40 miles an hour and 1/3 of the time at 80 miles an hour.

A-1.75
B-5.25
C-5.5
D-5.75
E-7.14
Always look at the answer choices.
Here, the answers represent the total time.
Since each speed is traveled for 1/3 of the total time, the correct answer must be easily divided by 3.
To divide a number easily by 3, the sum of its digits must be 3.
While B and E both satisfy this condition, 7.14 -- the value in E -- is far too messy to be the correct answer.
Thus, it is almost guaranteed that the correct answer is B.

Answer choice B: 5.25 hours
Time traveled at each speed = (5.25)/3 = 1.75 = 7/4 hours.
Distance traveled = (7/4)20 + (7/4)40 + (7/4)80 = 35+70+140 = 245.
Success!

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