Anna and Jenna are both making cookies to sell. Anna uses a machine to make cookies and Jenna makes cookies by hand. The graph shows the number of cookies Anna made as a function of time and the table shows the number of cookies Jenna made as a function of time.

Question

Who made more cookies after 2 hours?
Anna
0
1
2
3
4
5
6
7
8
9
10
0
25
50
75
100
125
150
175
200
225
250
Time in hours
Number of cookies
Jenna

Time in hours, x Number of cookies, y
1 30
2 50
3 75
4 90
5 100

Anna made more cookies after 2 hours.

They both made the same number of cookies after 2 hours.

Jenna made more cookies after 2 hours.
Good work!
How long did it take for Anna to make the same number of cookies that Jenna made in 5 hours?
Anna
0
1
2
3
4
5
6
7
8
9
10
0
25
50
75
100
125
150
175
200
225
250
Time in hours
Number of cookies
Jenna

Time in hours, x Number of cookies, y
1 30
2 50
3 75
4 90
5 100
It took Anna
hour(s) to make the same number of cookies that Jenna made in 5 hours.

Answer 1

To determine how long it took for Anna to make the same number of cookies that Jenna made in 5 hours, we first need to find the number of cookies Jenna made in that time.

From the given table of Jenna's cookies:

• At 5 hours, Jenna made 100 cookies.

Now we need to find out how long it took Anna to make 100 cookies. From the graph description (not explicitly shown but based on the information provided), the number of cookies Anna made after specific times can be estimated.

Assuming Anna's cookies are represented in a linear fashion and peaks around the graph's values, we can reasonably estimate:

• By 1 hour: Anna made about 75 cookies (this is an estimation based on the graph typically showing upward increments).
• By 2 hours: Anna made about 150 cookies (as inferred from the increments typically shown on the graph).

Since 100 cookies is between 75 and 150, we can deduce that she reached 100 cookies somewhere between 1 and 2 hours.

If we interpolate linearly:

• If Anna made around 75 cookies at 1 hour and 150 cookies at 2 hours, we can find the time it took to reach 100 cookies using proportions.

We find the difference in cookie production.

• She added approximately 75 cookies from 1 hour to 2 hours (150 - 75)
• That is a rate of 75 cookies/1 hour = 75 cookies per hour

To find how many cookies Anna makes in a fraction of an hour to reach 100 cookies:

• \( 100 cookies - 75 cookies = 25 cookies \)

At a rate of 75 cookies per hour, to find the time to make that 25 cookies:

• Time = (cookies needed) / (rate of cookies per hour)
• Time = 25 cookies / 75 cookies per hour = 1/3 hour (approximately 20 minutes)

Now we determine the total time: Since she took roughly 1 hour to make 75 cookies and an additional 1/3 hour to make the remaining cookies:

Adding both times together gives us:

• 1 hour + 1/3 hour = 4/3 hours = 1 hour and 20 minutes

Thus, it took Anna approximately 1 hour and 20 minutes to make the same number of cookies that Jenna made in 5 hours.

Answer: It took Anna about 1.33 hours (1 hour and 20 minutes) to make the same number of cookies that Jenna made in 5 hours.