Maria and josie are organizing a 5k run and donating all the proceeds to a local charity. as organizers, they’ll be doing a lot of work to make sure the event is well advertised in the community and that it goes off smoothly.

question 1
part a
one of maria and josie’s early tasks is printing and laminating signs to hang at local businesses around town. working alone, maria could print and laminate the signs in 4 hours. josie, however, has better laminating equipment, so she could get the job done by herself in 2 hours. if each works for the same amount of time, how long will it take them working together to print and laminate the signs? start by filling in the table with the missing values or expressions. note that rate of work is a unit rate that describes the amount of the job completed in one hour.

part b
use the table in part a to create an equation. then, solve it to find out how long will it take for maria and josie to complete the job together.

question 2
part a
maria and josie are also figuring out the dimensions of the runners’ corral at the start line. to accommodate the number of projected runners, they’ve determined that they need a minimum area of 29,040 square feet in the corral. they have 1,364 feet of temporary fence barriers to set up the corral. they are leaving one end of the rectangular corral open as shown in the image.

when the race is about to start, maria and josie will remove the fencing barriers on the start line. create an inequality that represents the relationship between the area of the space and the length of fencing needed.

part b
would a length of 650 feet meet the requirements for the runners’ corral? if so, what would the width be? justify your response with calculations.

question 3
part a
the registration period for the race is under way, and as the word is getting out, the number of participants registering is growing exponentially. the numbers from the first two days of registration are shown in the table.

use the data in the table and the general form of an exponential growth equation, y = a(1 + r)x, to write an equation modeling the exponential growth of registrations, where x is the number of days since registration opened, a is the initial number of registrations, r is the rate of growth of registrations per day, and y is the total number of registrations.

15 points pl! this is for a quiz me get a good grade!