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Class IV Inveractive Anglish Programing

Class III - Combined Rate and Relational Problems


Many story problems combine Class I and Class II equations. This happens when
the items in a rate problem are given in relational terms.  Class I problems
use rate equations of the form:
        rate X time = distance
Class II problems are concerned with calculating an entity such as a rate when
expressed in relational terms, i.e.
        unknown X factor + term = rate.
Combining the two gives
        (unknown X factor + term) X time = distance
The two equation chart header is:
                ---------------------------------------------------
                |unknown X factor + term = rate                   |
                |                          rate X time = distance |
                ---------------------------------------------------
                |        |        |      |      |      |          |
                ---------------------------------------------------                                                 
Equally likely, the time entity may be given in relational terms.  That is:
        rate X (unknown X factor + term) = distance
Rearranging 
        rate X time = distance
into
        time X rate = distance
for presentation reasons allows the two equation chart to be written as:
                ----------------------------------------
                |unknownXfactor+term=time              |
                |                    timeXrate=distance|
                ----------------------------------------
                |       |      |    |    |    |        |
                ----------------------------------------
The above are typical forms of a chart for Class III relational rate equation problems. To summarize how to solve relational rate problems: first, look for the relational terms to identify the relational factor Class I equation. Set up the chart with the general Class II relational equation solved for the common entity and align with the Class I equation. Then fill in the values.
Relational rate problems are easy to spot because they have relational clues - "more than," "as many as," etc. and deal with rate problems. For example, Pete takes twice as long to do a job as Joe. Together it takes them 3 hours. How long would it take each one alone?
This problem uses the Class I rate problem formula
                rate X time = effort.
However, the time is given in relative, not absolute, terms requiring a Class II relational equation. Chart generation for these problems is simply a matter of generating a common header from both class formulas. As a matter of convention, the relational equation is first, a factor only equation in this case:
        unknown X factor = time.
The term is "0" and does not need to be specified. It is easiest to arrange the equations so that the entity being related is the first factor of the rate equation so that it can be aligned with the right side of the relatonal equation. In this problem Pete's and Joe's times are being related, so the rate equation would be 
        time X rate = effort.
Combining the two and inserting the givens produces
                ------------------------------------------
                |        |unknownXfactor=time            |
                |        |               timeXrate=effort|
                ------------------------------------------
                |  Pete  |       |  2   |    |    |  1   |
                |   +    ---------------------------------
                |  Joe   |       |  1   |    |    |  1   |
                |   =    ---------------------------------
                |combined|       |      |  3 |    |  1   |
                ------------------------------------------
This chart is correct, but it is slightly different in table form (See Compound Column Names and/or Compound Row Names and Cell Names so that the computer can parse (understand) it.

Class IV problems require two tables.