The rate of doing work is the ratio of work and time. The time it will take for all of them to make the invitation cards is 1.2 hours.
<h3>What is the relation between work, rate, and time?</h3>
The rate of doing work is the ratio of work and time. Therefore, the relation between the work, rate of doing work and time is,
Rate of doing work = Work / Time
Assume the total work to be represented by x.
Given that It would take Stacey and Mia 4 hours each to do the job. Therefore, the rate at which Stacey and Mia both work can be written as,
Stacey's rate of working = Mia's rate of working = Work/time = x/4
Also given that Harper alone could do the job in 3 hours. Therefore, the rate at which Harper will work is,
Harper's rate of working = x/3
Now, the rate at which the three of them will work together is,
Rate of all three = (x/4) + (x/4) + (x/3)
= (3x/12) + (3x/12) + (4x/12)
= 10x/12
= 5x/6
Further, the time it will take for all of them to make the invitation cards are,
Time = Work/ Rate of working
Time = x/(5x/6) hours
Time = 6x/5x hours
Time = 1.2 hours
Hence, the time it will take for all of them to make the invitation cards is 1.2 hours.
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