Final answer:
The 4th runner must complete their 100-meter segment of the relay race in 52.365 seconds or less for the team to meet their goal of running the race in 210 seconds.
Step-by-step explanation:
To find the number of seconds, n, within which the 4th runner must finish for the team to meet their goal of completing a 400-meter relay race in 210 seconds, we can solve the equation (53.715 + 51.3 + 52.62) + n = 210.
- First, we add the split times for the first three runners: 53.715 + 51.3 + 52.62 = 157.635 seconds.
- Next, we subtract this sum from the total goal time: 210 - 157.635 = 52.365 seconds.
- The 4th runner must therefore complete their segment of the race in 52.365 seconds or less for the team to achieve their goal.