Jomo apologizes, JeffM exclaims, Subhotosh plots

Steven G

Elite Member
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Dec 30, 2014
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The equal button on a calculator can be used in a way that is inconsistent with the meaning of an equal sign in mathematics. Moreover, decimal hours are not the same as hours and minutes.

Both your methods will work if done properly.

Method 1: Convert hours and minutes to minutes, subtract, and convert minutes to hours and minutes.

Convert 33 hours 7 minutes to minutes.

\(\displaystyle 33 \times 60 = 1980.\)

\(\displaystyle 1980 + 7 = 1987.\)

Convert 6 hours and 50 minutes to minutes.

\(\displaystyle 6 \times 60 = 360.\)

\(\displaystyle 360 + 50 = 410.\)

Subtract.

\(\displaystyle 1987 - 410 = 1577.\)

So far you were doing fine, and you showed the right sequence of keys for a calculator although it is not proper math notation.

You then calculated hours, which makes good sense, but a calculator will usually give you a decimal approximation rather than an exact fraction and will not break hours into hours and minutes.

\(\displaystyle \dfrac{1577}{60} = 26 + \dfrac{17}{60} \approx 26.28.\)

But that is an answer in hours only, not hours and minutes.

\(\displaystyle \dfrac{17}{60} \text { hours is } 17 \text { minutes.}\)

So the correct answer is 26 hours and 17 minutes, which is approximately 26.28 hours.

Method 2: Work with hours and minutes separately.

Start with minutes. You can't subtract 50 from 7 within the non-negative numbers. So you must "borrow" some minutes from the hours. Subtracting 1 hour from the hours let's you add 60 to the minutes.

\(\displaystyle 33 \text { hours and } 7 \text { minutes is the same as } 32 \text { hours and } 67 \text { minutes.}\)

\(\displaystyle 67 \text { minutes } - 50 \text { minutes } = 17 \text { minutes.}\)

OK you are done with minutes. Now for hours, but remember you "borrowed" one hour.

\(\displaystyle 32 \text { hours } - 6 \text { hours } = 26 \text { hours.}\)

The correct answer is 26 hours and 17 minutes, which is NOT 26.17 hours.
JeffM, somehow I did not see your reply before posting mine which is quite similar to yours. Sorry about that.
 
JeffM, somehow I did not see your reply before posting mine which is quite similar to yours. Sorry about that.
Not a problem. We are all trying to help people with math: it is not a contest.
 
Oh my, a puzzle! Can you send to the corner someone already there?
Yes, it can be done. It is called corner2 which is better known as a square corner.
 
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