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21 Aug 2013, 20:56
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Simplest way to the answer that I found.....
s just has to equal 2, and s+1 just has to equal 3. If average speed = 2.8, he has to be at s(2) for 1/5 of time, and s+1(3) for 4/5 of time.
Time is not defined, only the average, so lets say the total time was 5 hours, so in one hour he walked 2 miles, then in each of the other four hours he walked 3 miles, 2+3+3+3+3=14.
What fraction of the total distance did he walk at s(2), is equal to 2 miles / 14 miles = 1/7
s just has to equal 2, and s+1 just has to equal 3. If average speed = 2.8, he has to be at s(2) for 1/5 of time, and s+1(3) for 4/5 of time.
Time is not defined, only the average, so lets say the total time was 5 hours, so in one hour he walked 2 miles, then in each of the other four hours he walked 3 miles, 2+3+3+3+3=14.
What fraction of the total distance did he walk at s(2), is equal to 2 miles / 14 miles = 1/7
m3equals333
06 Mar 2014, 23:55
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Is there an algebraic way to solve for s (or even solve directly for the distance ratio) if it wasn't immediately apparent to us that 2.8 is between s and s+1 and s is an integer so it has to be 2?
I attempted to do this and it not only turned into a mess, but also didn't seem possible? Knowing that s=2 is definitely the key, but I was curious if there is a feasible workaround, thanks.
I attempted to do this and it not only turned into a mess, but also didn't seem possible? Knowing that s=2 is definitely the key, but I was curious if there is a feasible workaround, thanks.
07 Mar 2014, 09:04
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m3equals333
I wrote this question and I will tell you what my intent was in writing it - I wanted to make people use logic. I wanted them to use deduction on the given data. Use of logic greatly simplifies many high level GMAT questions. So I tried to force them to deduce this vital piece of information - the two speeds must be 2 and 3. You can't put everything given to you in terms of an equation and that is what I tried to exploit.
Even if you don't start with it, at some point you will require some deduction.
For example, say you use weighted averages. 2.8 is the average speed. Weights in case of speeds are the time taken in the two cases.
Ratio of time spent while its sunny and time spent while its cloudy = \(\frac{Ts}{Tc} = \frac{(s+1) - 2.8}{2.8 - s}\)
\(\frac{Ts}{Tc}= \frac{s - 1.8}{2.8 - s}\)
Now what can you say about s?
s must be greater than 1.8 since the fraction cannot be negative. It must also be less than 2.8 since the fraction cannot be negative.
Since s must be an integer, it must be 2. So (s+1) must be 3.
