The equation y = 1.6x represents the number of laps Henry can swim over time, where y is the number of laps and x is time in minutes. The table shows the number of laps Larry can swim over time.


How many laps can each boy complete per minute, and who can swim laps at a faster rate?

Henry:
laps per minute

Larry:
laps per minute

The boy who swims at a faster rate is
. (Type H for Henry or L for Larry)


Larry
Time (min) 2.5 4 5.5 8
Laps completed 4.5 7.2 9.9 14.4

Assuming the data for Larry is linear,

slope = (14.4 - 9.9)/(8-5.5)
= 1.8

Larry's equation would be y = 1.8x

So Henry can do 1.6 laps per minute
and Larry can do 1.8 laps per minute

so who do you think can swim faster?

Larry

To find the laps per minute for Henry, we can take the coefficient of x in the equation y = 1.6x. In this case, the coefficient is 1.6.

Therefore, Henry can swim 1.6 laps per minute.

To find the laps per minute for Larry, we can calculate the change in laps divided by the change in time for each interval.

For the interval from 2.5 minutes to 4 minutes, Larry swam 7.2 - 4.5 = 2.7 laps in 1.5 minutes, so he can swim 2.7/1.5 = 1.8 laps per minute.

For the interval from 4 minutes to 5.5 minutes, Larry swam 9.9 - 7.2 = 2.7 laps in 1.5 minutes, so he can swim 2.7/1.5 = 1.8 laps per minute.

For the interval from 5.5 minutes to 8 minutes, Larry swam 14.4 - 9.9 = 4.5 laps in 2.5 minutes, so he can swim 4.5/2.5 = 1.8 laps per minute.

Since Larry's laps per minute is constant at 1.8 for all intervals, we can conclude that Larry can swim 1.8 laps per minute.

Now, we compare the laps per minute for Henry and Larry. We have:

Henry: 1.6 laps per minute
Larry: 1.8 laps per minute

Since 1.8 is greater than 1.6, Larry can swim laps at a faster rate than Henry.

Therefore, the boy who swims at a faster rate is Larry (L).

To find the number of laps each boy can complete per minute, we need to divide the number of laps by the time in minutes. Let's calculate it for each boy.

For Henry:
From the equation, we know that Henry can swim 1.6 laps per minute.

For Larry:
To find the laps per minute for Larry, we divide the number of laps completed by the time in minutes for each data point in the table.

For the first data point:
Laps per minute = Laps completed / Time (in minutes) = 4.5 / 2.5 = 1.8 laps per minute.

For the second data point:
Laps per minute = Laps completed / Time (in minutes) = 7.2 / 4 = 1.8 laps per minute.

For the third data point:
Laps per minute = Laps completed / Time (in minutes) = 9.9 / 5.5 = 1.8 laps per minute.

For the fourth data point:
Laps per minute = Laps completed / Time (in minutes) = 14.4 / 8 = 1.8 laps per minute.

Therefore, Larry can swim at a rate of 1.8 laps per minute.

To determine who swims laps at a faster rate, we compare the laps per minute for Henry and Larry. Both Henry and Larry can swim laps at a rate of 1.8 laps per minute. So, they have the same swimming rate.

Therefore, the answer is:
Henry: 1.6 laps per minute
Larry: 1.8 laps per minute
Both Henry and Larry can swim at the same rate.