Please help!

[cstogsdill60]

if it takes 115 seconds to pave 36 feet how many hours would it take to pave 89 miles?
any help is greatly appreciated

 

[tkhunny]

Have you met "Dimensional Analysis"? It is wonderful. Just multiply by Unity!

\(\displaystyle \frac{36\;ft}{115\;sec}*\frac{60\;sec}{1\;min}*\frac{60\;min}{1\;hr}...\)

Okay, I have it changed to ft/hour. You take a shot at ft into miles.

 

[mmm4444bot]

There is another approach that accomplishes the same conversions as dimensional analysis, but is less formal.

Look up how many feet there are in one mile. Multiply this number by 89, and you will have converted 89 miles into feet.

Divide this total number of feet by 36, to find out how many sections there are that require 115 seconds each to pave.

Multiplying the total number of sections by 115 gives you the total paving time in seconds.

Divide this by the number of seconds in one hour, and you will have converted the time to pave 89 miles from seconds into hours.

 

[jsterkel]

Labels

To expand on Tkhunny's post a bit, we can multiply any number times 1 and not change the number.

5*1 = 5
12 * 1 = 12

We could also multiply a number by a fraction that equals 1 and not change the number.
\(\displaystyle 12 * \frac{2}{2} = 12 * 1 = 12
\)

We can go a step further and multiply a number by a fraction that has labels.
\(\displaystyle 12 *\frac{1\;min}{1\;min} = 12 * 1 = 12
\)

In this case, the ratio \(\displaystyle \frac{1\;min}{1\;min} \) simplifies to 1.


Since there are 60 seconds in 1 minute, we can convert minutes to seconds in this way:
\(\displaystyle 12 min*\frac{60\;sec}{1\;min} = \frac{12 min * 60 sec\; }{1\;min} = \frac{12 * 1 min* 60 sec\; }{1\;min} \)

The ratio \(\displaystyle \frac{1\;min}{1\;min} \) simplifies to 1/1, leaving us with
\(\displaystyle \frac{12 * 60 sec\ * 1 }{1} = 12 * 60 sec = 720 sec \)



That is what Tkhunny is doing with this conversion:

\(\displaystyle \frac{36\;ft}{115\;sec}*\frac{60\;sec}{1\;min}*\frac{60\;min}{1\;hr}...\)

 

[tkhunny]

multiply any number times 1

Good work, jsterkel. But never say that again.

 

[jsterkel]

Good work, jsterkel. But never say that again.

Could you suggest wording that is more correct? Thanks!

Thanks for the kind words!

 

[tkhunny]

Yes,"...multiple any number by 1..."

I went to a 6th grade open house the other day. The new math teacher, trying to impress the students of the importance of homework, said, "If you take that daily point total and times it by 35...". Now, this is worse than what you said. The 6th grade teacher was just awful. In yours, the mere presence of the word "times", simply was a little jarring.

 

[burakaltr]

if it takes 115 seconds to pave 36 feet how many hours would it take to pave 89 miles?
any help is greatly appreciated

Since the rate is invariant

Find rate

rate * time = paved miles

Make required unit changes and find out !


Good Luck !

Also you can use linear proprtionality.

 

[lookagain]

We could also >>> multiply a number by a fraction <<< that equals 1 and not change the number.



We can go a step further and >>> multiply a number by a fraction <<< that has labels.

jsterkel,

note that in each of these two sentencs of yours, that you used correct
phrases.

You did not type the incorrect "multiply a number times a fraction" phrase.

 

[mmm4444bot]

Another mathematical faux-pas of the 'times':

"x^3 is x multiplied by itself three times"