Imagine that you are in a bleachers watching a swim meet in which your friend is competing in the freestyle event. At the instant the starting gun fires, the lights go out! When the lights come back on, the timer on the scoreboard records 86s. You observe your friend is now about halfway along the length of pool, swimming in a direction opposite to that in which he started. The pool is 50 m long.

what are two possible distances that you might infer your friends swam while the lights were out, given the average velocity is 0.29 meters per second

The two possible distances that you might infer your friends swam while the lights were out are 25 m and 75 m.

Explanation:

So you have to measure the distance covered by your friend in a time gap of 86 s. And the average velocity is given as 0.29 m/s.

Then as per the mathematical calculation of velocity, distance can be measured as the product of velocity with time interval.

Distance = Velocity × Time Interval

Distance = 0.29 m/s×86 s = 24.94 m.

So based on this calculation, one of the possible distance inferred by you will be 24.94 m.

Another possible distance can be guessed from the statements provided. So if the length of pool is 50 m, then covering halfway in opposite direction to his starting direction means completion of one full length i.e., 50 m and then halfway of that 50 m which is 25m, so totally 50 +25 = 75 m.

So in other way, we can assume that your friend has covered 75 m distance during the light out.

Thus, the two possible distances that you might infer your friends swam while the lights were out are 25 m and 75 m.