To compare the number of sit-ups Jacob and Jordan can do in 2 1/2 minutes, we need to convert their current rates to the same unit of time. Since 2 1/2 minutes is the same as 150 seconds, we can use unit rates to find the number of sit-ups they can do per second.
Jacob's rate is 39 sit-ups in 30 seconds, so his unit rate is:
39/30 sit-ups per second
Simplifying the fraction, we get:
13/10 sit-ups per second
Jordan's rate is 59 sit-ups in 50 seconds, so his unit rate is:
59/50 sit-ups per second
Multiplying the numerator and denominator by 3, we get:
177/150 sit-ups per second
Now we can use these unit rates to estimate the number of sit-ups Jacob and Jordan can do in 2 1/2 minutes:
Jacob's estimated number of sit-ups = unit rate × time
= (13/10 sit-ups per second) × (150 seconds)
= 195 sit-ups
Jordan's estimated number of sit-ups = unit rate × time
= (177/150 sit-ups per second) × (150 seconds)
= 177 sit-ups
Based on these estimates, Jacob is likely to do more sit-ups in 2 1/2 minutes than Jordan, since he can do approximately 18 more sit-ups (195 - 177).
Therefore, Jacob is likely to do more sit-ups in 2 1/2 minutes than Jordan.