Question

Jackson and his grandfather constructed a model for a birdhouse. Many of their neighbors offered to buy the birdhouses. Jackson decided that building birdhouses could help him earn money for his summer camp, but he is not sure how long it will take him to finish all of the requests for birdhouses. If Jackson can build 7 birdhouses in 5 hours, write an equation that will allow Jackson to calculate the time it will take him to build any given number of birdhouses, assuming he works at a constant rate.

a. Write an equation that you could use to find out how long it will take him to build any number of birdhouses.
b. How many birdhouses can Jackson build in 40 hours?
c. How long will it take Jackson to build 35 birdhouses? Use the equation from part (a) to solve the problem.
d. How long will it take to build 71 birdhouses? Use the equation from part (a) to solve the problem.

Answer 1

a) y(t) = (7/5)×t

b) He can build 56 birdhouses in 40 hours.

c) It will take for Jackson 25 hours to build 35 birdhouses.

d) It will take for Jacson 50.7 hours to build 71 birdhouses.

Explanation:

a) According to the exercise , the rate is constant the equation is going to have the following form:

y(t) = a×t + b

where y(t) is the number of birdhouses that Jackson can build in a time t. a and b are some constants to which we need to find their value.

Since when t = 0 there are no birdhouses built, y(0) = 0

0 = a×0 + b

0 = b

Since Jackson can build 7 birdhouses in 5 hours, y(5) = 5

7 = a×5

a = 7/5

The equation is going to be:

y(t) = (7/5)×t

b) we need to find y(t) when t=40

y(40) = (7/5)×40 = 56

c) we need to find t when y(t)=35

35 = (7/5)×t

we multiply by five and divide by 7

t = 35×5÷7 = 25

d) we need to find t when y(t)=71

71 = (7/5)×t

we proceed as in c)

t = 71×5÷7 = 50.7