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The question is:

An empty pool being filled with water at a constant rate takes 8 hours to fill to \frac{3}{5} of its capacity.How much more time will it take to finish the filling the pool? (Ans 5 hr 20min)

Now here is how I am solving it:

The entire time required to fill the pool would be $\frac{40}{3}$ hours or $13$ hours and $1$ min

So how much more time would be $(13-8)$ hours will be $5$ hours and $1$ min.Why am i getting the wrong answer. I would appreciate it if someone could tell me where I am going wrong

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$40/3$ hours is 13 hours and $\bf 20$ minutes ($13$ hours and $1/3$ hours). –  David Mitra Sep 14 '12 at 0:51
    
@DavidMitra could you please tell me how you got 13 hours and 20 min ? I get a remainder of 1 or 13$\frac{1}{3}$$when I divide 40 by 3 ? –  MistyD Sep 14 '12 at 0:56
    
Yes, $40/3=13+1/3$. So it's $13$ and $1/3$ hours. $1/3$ of an hour is $20$ minutes. –  David Mitra Sep 14 '12 at 1:00
    
Oh okay. (1/3) of an hour. Now I get it thanks for clearing that up –  MistyD Sep 14 '12 at 1:01

2 Answers 2

up vote 1 down vote accepted

Your basic reasoning is correct; however, you made two errors in converting $40/3$ hours into hours/minutes. First, $40/3$ is not $13.1$ (as you seem to imply), it's $13.\overline3$ or $13\,{1\over3}$. Second, the decimal part of this is not minutes, it's still hours. So you have $13$ and $1/3$ hours. $1/3$ of an hour is $20$ minutes. So, $40/3$ hours is $13$ hours and $20$ minutes.

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How did you reason: "the entire time required to fill the pool would be 40/3 hours or 13 hours and 1 min."?

Hint: 40/3 seems right.

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Because if $\frac{3}{5}$ requires $8$ hours then $1$ would require $\frac{5\times8}{3}$ ? Am I wrong ? –  MistyD Sep 14 '12 at 0:54
    
Yea, that part is right, what I meant is what about the 13 hours and 1 min? –  Alex R. Sep 14 '12 at 1:03
    
That is where i was wrong. I thought the remainder represented a minute. –  MistyD Sep 14 '12 at 1:04
    
Actually is 1/3 of an hour –  MistyD Sep 14 '12 at 1:05

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