The return-air ventilation duct in a home has a cross-sectional area of 900 cm^2. the air in a room that has dimensions 5.0 m x 11.0 m ×x 2.4 m is to be completely circulated in a 50-min cycle.
1) what is the speed of the air in the duct? (express your answer to two significant figures.)

To solve the problem it is necessary to apply the concepts related to the flow rate of a fluid.

The flow rate is defined as

Where,

v = Average speed (m / s)

And also as

Where,

V = Volume

t = time

Let's start by finding the total volume according to the given dimensions, that is to say

The entire cycle must be completed in 50 min = 3000s

In this way we know that the must be filled in 3000s, that is to say that there should be a flow of

Using the relationship to find the speed we have to

Replacing with our values,

Therefore the air speed in the duct must be 4.88m/s