Edward A. answered • 9h

Math Tutor, Retired Computer Scientist and Technical Communicator

Khim, this shows the importance of checking the answer. If Laramie can do the job in 2-1/2 hours, why would it take longer (3-1/4 hours) to do it when Lyn is helping?

Khim, the key to “shared work” problems is to understand Work, Rate, and Time.

Work = Rate * Time

( w = r t )

Work is the amount of effort expended or material produced.

Rate is how fast someone can do the work ( what fraction of the work gets done in an hour. Or how many jobs per month, etc.)

Time is the amount of time it takes someone to get the job done.

If the amount of work is 1 job, then the rates and times are reciprocals:

1 = RT or R = 1/T or T = 1/R

In this problem,

Ta = 2.5 (the amount of time Laarnie takes)

Ty = 4 (The amount of time Lyn takes)

How long does it takes when they work together? To answer that, we have to convert Times to Rates.

1 job = Rate * Time = (Ra + Ry)* T

But how do we get Rates from Times?

Ra = 1/Ta

Ry = 1/Ty

So substitute those rates into the equation.

1 = (1/Ta + 1/Ty) * T

1= (1/2.5 + 1/4) * T

Now add the fractions and solve for T

1= (6.5/10)T

T = 10/6.5 = 20/13 hours

This makes sense: it should take less time for both of them to do the job than either one alone.