Edward A. answered • 12/06/19
Clear tutor: Excel formulas, graphs, pivot tables, macros, What-Ifs
Shane,
Shared work problems
These problems generally have a constraint about time spent working together.
The fundamental formula is
Work = rate * time
As always, give names to all quantities.
Let RS be the rate at which Sally can paint the house (that is, what fraction of a house can she paint in an hour)
Let RJ be the rate at which John can paint the house
Let TS be the time it takes Sally to do the work
Let TJ be the time it takes John to do the work
Since Work = Rate * Time , let’s abbreviate this as
W=RT
Sometimes you need to know the rate, so solve for R:
R = W/T
Sometimes you need to know the time, so solve for T:
T = W/R
Often, the amount of work is 1...1 house painted, 1 print run printed, etc.
In those cases, the Rates and Times are reciprocal.
Here are the relationships
TS = 1/RS
TJ = 1/RJ
Sally can paint a house in 4 hours and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
TS = 4
TJ = 6
Therefore
RS = 1/4
RJ = 1/6
Let T be the time it takes for them to paint the house together
1 = T*RS + T*RJ
Factor T out
1 = T(RS + RJ)
solve for T
T = 1 / (RS + RJ)
T = 1 / (1/4 + 1/6)
= 1/(5/12) = 12/5 hours
If you have more questions, please ask.
Edward A.
Shane, I realize that I didn’t answer your question directly. Here goes: The reason I flipped an expression over is because I was solving the equation 1 = T*R for T. That resulted in T = 1/R. R was rather complicated, consisting of the sum of two reciprocals. That R eventually evaluated to 5/12. Therefore 1/R was 12/5. So I didn’t follow a recipe to flip over an answer. Instead, the solution to T = 1/R demands that I flip over R at the end. Does that help answer your question?12/06/19