Question

a team of swimmers is training for a swim meet. the table shows the number of laps each person has swum so far and how long the laps took.

name	laps	time (minutes)
julian	1	1
seth	3	6
bennett	7	21
taylor	4	7

the relationship between time and the number of laps is not proportional across all swimmers. which two swimmers swam at the same rate (had time and laps in the same proportion)?

a. jonathan and julian
b. seth and bennett
c. julian and taylor
d. jonathan and seth
e. julian and seth

Explanation:

Step1: Calculate rate for each swimmer

Rate is time divided by laps (or laps divided by time, as long as consistent). Let's use time/laps.

• Jonathan: $\frac{4}{2} = 2$ minutes per lap.
• Julian: $\frac{1}{1} = 1$ minute per lap.
• Seth: $\frac{6}{3} = 2$ minutes per lap.
• Bennett: $\frac{21}{7} = 3$ minutes per lap.
• Taylor: $\frac{7}{4} = 1.75$ minutes per lap.

Step2: Compare rates

Jonathan and Seth both have a rate of 2 minutes per lap. Also check option D: Jonathan (2) and Seth (2) match. Wait, also check option B: Seth (2) and Bennett (3) no. Wait, wait, my calculation for Seth: 6/3=2, Jonathan:4/2=2. So Jonathan and Seth have same rate. But let's recheck the options. Wait the options: D is Jonathan and Seth? Wait the original options:

Wait the user's image: options are A. Jonathan and Julian, B. Seth and Bennett, C. Julian and Taylor, D. Jonathan and Seth, E. Julian and Seth? Wait maybe I misread. Wait the user's text:

Wait the problem's options:

A. Jonathan and Julian

B. Seth and Bennett

C. Julian and Taylor

D. Jonathan and Seth

E. Julian and Seth? Wait no, the user's image shows:

Wait the user's provided image:

Options:

A. Jonathan and Julian

B. Seth and Bennett

C. Julian and Taylor

D. Jonathan and Seth

E. Julian and Seth? Wait no, the user's text:

Wait the user's question: "Which two swimmers swam at the same rate..."

Wait my calculation:

Jonathan: 4 min / 2 laps = 2 min per lap.

Seth: 6 min / 3 laps = 2 min per lap.

So Jonathan and Seth (option D) have same rate. Wait but let's check again.

Wait Bennett: 21/7=3, so no. Julian:1/1=1, Taylor:7/4=1.75. So Jonathan (2) and Seth (2) match. So the correct option is D. But wait the user's image has a yellow highlight on B, but that's a mistake. Wait no, maybe I miscalculated Seth. Wait 6 laps? No, Seth's laps are 3, time 6. So 6/3=2. Jonathan: 4/2=2. So same rate. So the correct answer is D. But let's check the options again.

Wait the user's options:

A. Jonathan (2) and Julian (1) → no.

B. Seth (2) and Bennett (3) → no.

C. Julian (1) and Taylor (1.75) → no.

D. Jonathan (2) and Seth (2) → yes.

E. Julian (1) and Seth (2) → no.

So the correct answer is D. But wait the user's image has B highlighted, but that's incorrect. So the correct option is D.

Wait but maybe I used laps/time instead. Let's try laps/time (laps per minute).

• Jonathan: 2/4 = 0.5 laps per min.

• Julian: 1/1 = 1 lap per min.

• Seth: 3/6 = 0.5 laps per min.

• Bennett:7/21=1/3≈0.333.

• Taylor:4/7≈0.571.

So Jonathan (0.5) and Seth (0.5) have same rate (laps per minute). So yes, Jonathan and Seth (option D) are same. So the correct answer is D.

Answer:

D. Jonathan and Seth