Question

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?

Answer 1

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.

What is the relation between work, rate, and time?

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:

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