Answer
Zina and Rachel will take (3/4) hour or 0.75 hour to build the model skyscraper working together simultaneously.
Explanation
Let the total work to be done in building the model skyscraper be x.
The question tells us that it takes Zina 1 hour to finsh the model skyscraper.
And Rachel takes 3 hours to finish the model of the skyscraper.
Since Rate of work done = (Workdone)/(time Taken)
For Zina,
Workdone = x
Time Taken = 1 hour
The rate at which Zina completes the model of the skyscraper is given as
Zina's workrate = (x/1) = x per hour
For Rachel,
Workdone = x
Time Taken = 3 hours.
The rate at which Rachel completes the model of the skyscraper is given as
Rachel's workrate = (x/3) = (x/3) per hour
So, if Zina and Rachel work together build the model skyscraper to finish, let the time that will take be t.
This means that Zina and Rachel will have to both work simultaneously for t hours in order for their joint work to complete the model skyscraper.
Recall that
Rate of work done = (Workdone)/(Time Taken)
By cross multiplying, we can easily show that
Workdone = (Rate of work done) × (Time taken)
So, we then calculate the workdone by Zina and Rachel in t hours respectively, knowing that the sum of those two quantities should be equal to the total work required to build the model skyscraper (x).
Workdone by Zina in t hours = x × t = (xt)
Work done by Rachel in t hours = (x/3) × t = (xt/3)
Total workdone by Zina and Rachel = (xt) + (xt/3) = x
This equation can then be solved for t mathematically
(xt) + (xt/3) = x
(4xt/3) = x
Cross multiply
4xt = 3x
Divide both sides by 4x
(4xt/4x) = (3x/4x)
t = (3/4) hour
Hence, Zina and Rachel will take (3/4) hour or 0.75 hour to build the model skyscraper working together simultaneously.
Hope this Helps!!!