How to set up these ratios?

Here's a question while reading my textbook:

For about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What are the ratios of (a) the French decimal week to the standard week and (b) the French decimal second to the standard second? Assume that the definition of a "day" remains the same.

The problem is, I have a very shaky foundation in Algebra and this is a Physics class. From Cal+ I'm fine, but setting up basic stuff using Algebra is hard for me. Any idea how I would set this up? I'm not looking for an answer I'm looking for some help understanding how this should done. Thank you.

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One standard week is 7 days. One French revolutionary week is 10 days. Thus

$$\frac 1 {10}\text{ French weeks} = 1\text{ day} = \frac 1 7\text{ standard weeks}.$$

Multiply both sides by 10 to get

$$1\text{ French week} = \frac {10} 7\text{ standard weeks}$$

or

$$\frac{1 \text{ French week}}{1 \text{ standard week}} = \frac {10} 7.$$

One day is $60 \times 60 \times 24 = 86400$ standard seconds, or $100 \times 100 \times 10 = 100000$ French revolutionary seconds. Can you find the rest of the answer yourself from here?

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Yep that's put me on my way. Thanks! – Rampage Aug 27 '11 at 18:30

There are slightly less than 16% more "ticks" on a French Revolutionary clock, (during one complete revolution of our planet ), than on the Standard Time clocks. Therefore; the actual "duration" of time between ticks, must be shorter on the French clock.(0,864), as compared to (1.000, on the Standard clock. Observation of both clocks together, will bear the above as truthful. Keep in mind. 16% is quite subtle when watching side by side ticking clocks. That tests, ones ingenuity & patients. Have fun.

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Here our constant for the calculation is a "DAY". so we ahave to be able to change our measurments in a "DAY".

1. Ratio of a French decimal week(W') to standard week(W)\

     1W'= 10 DAYS,        1W= 7 DAYS


Ratio= 1W'/1W = 10DAYS/7DAYS ~ 1.43-------------------------------ANSWER

2. Ratio of a French decimal second(S') to standard second(S)

    1 DAY = 10 * 100 * 100 S',      1DAY = 24 * 60 * 60 S
1DAY= 100000 S'                1DAY =86400 S


Now lets calculate the value of S' and S interms of a "DAY".

       1 DAY =100000 S'               1DAY = 86400 S
?   =   1 S'                  ?   =   1 S
1 S' = 1/100000 DAY            1 S = 1/86400 DAY


Ratio = 1S'/1S = 1/100000 DAY ÷ 1/86400 DAY = 0.864--------------ANSWER.

ANY KIND OF COMMENT IS WELCOME.

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the french decimal weak & the standard weak. ratio of french decimal weak & standard weak=10:7 =(10)(10)(100)(100)/(7)(24)(60)(60) =1.6534answer ratio of french decimal second to the standard sec. 100:60 50:30 25:15 5:3answer