Question

Everyone at camp takes turns being on lunch duty. You and your friend are in charge of making sandwiches. you both can make 1 sandwich in two minutes. Your friend arrives 10 minutes earlier than you and starts making sandwiches.

a. write equations that model the number of sandwiches made as a function of the number of minutes it takes you and your friend to each make sandwiches.

b. how many sandwiches will each of you make in 20 minutes?

c. how are the graphs of the equations from part (a) related? justify your answer.

Answer 1

Answer To (b): 10 sandwiches in 20 minutes. But If Your Friend Arrived 10 Minutes Earlier, Then He Can Make 20 Sandwiches In The 20 Minutes That You Are There. If He Started When He Arrived And The Twenty Minutes Started Then, You Can Only Make 5.

Answer 2

a) y1 = 0.5*t, y2 = 0.5*(t - 10)

b) 10 and 5

c) the graph of y2 is graph of y1 shifted 10 units to the right

Explanation:

a) Taking t = 0 the time your friend arrived, then the sandwiches (y1) made by your friend were:

t y1

0 0

2 1

4 2

and so on. The equation that relates this two variables is: y1 = 0.5*t

The sandwiches (y2) made by you were:

t y1

0 0

2 0

4 0

6 0

8 0

10 0

12 1

14 2

and so on. The equation that relates this two variables is: y2 = 0.5*(t - 10), where only the positive y2 values must be considered.

b) Replacing with t = 20 in each equation, we get:

y1 = 0.5*20 = 10

y2 = 0.5*(20 - 10) = 5

c) If f(x) is the parent function, a shift n units to the right is f(x - n). Replacing t with (t - 10) in y1 we get y2, then, the graph of y2 is graph of y1 shifted 10 units to the right.