Eight engineers with 2 technicians can design a house in 7 hours, which 25 engineers with 13 technicians can do in 2 hours. What fraction of the whole work, can be done in 1 hour by 11 engineers with 20 technicians?

To solve this problem, we first need to understand that the work done is proportional to the number of workers and the time they work.

Step 1: Find the work rate of the engineers and technicians.

We know that 8 engineers and 2 technicians can design a house in 7 hours. So, their combined work rate is 1 house/7 hours = 1/7 houses per hour.

Similarly, 25 engineers and 13 technicians can design a house in 2 hours. So, their combined work rate is 1 house/2 hours = 1/2 houses per hour.

Step 2: Set up equations to find the individual work rates.

Let E be the work rate of an engineer and T be the work rate of a technician. We can set up the following equations based on the information given:

8E + 2T = 1/7 (equation 1) 25E + 13T = 1/2 (equation 2)

Step 3: Solve the equations to find E and T.

You can solve these equations using substitution or elimination method. Once you find the values of E and T, you can find the work rate of 11 engineers and 20 technicians.

Step 4: Find the work done in 1 hour by 11 engineers and 20 technicians.

Multiply the work rates of the engineers and technicians by their respective numbers and add them together. This will give you the fraction of the whole work that can be done in 1 hour by 11 engineers and 20 technicians.