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gogolik [260]
1 year ago
10

Stacey, Mia, and Harper want to make invitation cards for the annual school dance. It would take Stacey and Mia 4 hours each to

do the job and Harper alone could do the job in 3 hours. If all work together, how long will it take them to make the invitation cards?
Mathematics
1 answer:
Reptile [31]1 year ago
5 0

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.

Learn more about Work, time and rate here:

brainly.com/question/23308203?referrer=searchResults

#SPJ1

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