Answer: To find the missing value in the table that represents the part of the floor Jasper will install when working together with Yolanda, we can use the concept of rates and work.
Let's denote the missing value as "x" representing the part of the floor Jasper will install when working with Yolanda.
According to the given information:
Jasper's rate of work is 1/7 of the floor per hour.
Jasper works for 3 hours.
Therefore, the part of the floor Jasper can install when working alone is:
Jasper's work = (Rate of work) * (Time) = (1/7) * 3 = 3/7
Now, let's consider Yolanda's rate of work. It is represented by "r," and she works for 3 hours. So, the part of the floor Yolanda can install is 3r.
When Jasper and Yolanda work together, their work rates add up. Therefore, the combined work rate when working together is:
Combined rate = Jasper's rate + Yolanda's rate
= 1/7 + r
Working together, they complete the entire floor in 3 hours. So, the equation can be written as:
(Combined rate) * (Time) = 1
(1/7 + r) * 3 = 1
Solving the equation:
3/7 + 3r = 1
3r = 1 - 3/7
3r = 4/7
r = (4/7) / 3
r = 4/21
Therefore, the missing value representing the part of the floor Jasper will install when working with Yolanda is:
Jasper's part = Jasper's rate * Time = (1/7) * 3 = 3/7
So, the missing value is 3/7, which is the part of the floor Jasper will install when working with Yolanda.