Question

At the beginning of the semester students reported that they spend an average of 5 hours per day watching television, decreasing at an average rate of 30 minutes per week. Professors reported that they spend an average of 1 hour per day watching television, increasing at an average rate of 30 minutes per week. (Source: Blitzer: Thinking Mathematically, 2019) a. Write a function, S, for the amount of time students watch television during week, x. b. Write a function, P, for the amount of time professors watch television during week, x. C. By which week do students and professors both watch the same number of hours of television? How many hours?

Answer 1

After 29 week both watch 21 hours of television per week.

Explanation:

Consider the provided information.

Part (A)

It is given that At the beginning of the semester students reported that they spend an average of 5 hours per day watching television

That means they spent 5×7 = 35 hours in first week.

Then decreasing at an average rate of 30 minutes per week.

In week 2, it will be 34.5 hours per week.

In 3rd week, it will be 34 hours per week and so on.

For x weeks the required equation will be:

S = 35 - 0.5(x-1)

S = 35.5 - 0.5x

Part (B)

Professors spends 1 hour per day in a week he spent 1×7=7 hours.

For 2nd week, it will be 7.5 hours per week.

For 3rd week, it will be 8 hours per week and so on.

For x weeks the required equation will be:

P = 7 + 0.5(x-1)

P = 6.5 + 0.5x

Part (C)

Equate the equations

35.5 - 0.5x = 6.5 + 0.5x

0.5x + 0.5x = 35.5 - 6.5

x = 29

Now substitute x=29 in P= 6.5 + 0.5x

P = 6.5 + 0.5(29)

P = 6.5 + 14.5

P = 21

Thus, after 29 week both watch 21 hours of television per week.