Fred can paint a house in 10 hours. Together, pat and Fred can paint a house in 8 hours. Which equation, when solved will produce the number of hours need for pat to paint the house alone

Pat t2 = 40 hrs

Step-by-step explanation:

Given:-

- Fred can paint a house in t1 = 10 hours.

- Pat can paint a house in t2 hours.

- pat and Fred can paint a house in T = 8 hours.

Find:-

Which equation, when solved will produce the number of hours need for pat to paint the house alone

Solution:-

- The number of people working on a particular activity " painting a house " is inversely proportional to time taken to complete the activity. tn = T. The relation for individual time taken ti to complete an activity.

                              Sum ( 1 / ti ) = 1 / T

Where, ti = The individual time for (ith) person

            T = The total time taken to complete the time by i = n number of people.

- For n = 2,

                              1/t1 + 1/t2 = 1/T

                              1/10 + 1/t2 = 1/8

                              1 / t2 = 0.025

                              t2 = 40 hrs

- It takes Pat t2 = 40 hrs to complete painting the house.