Juan is planning to run a marathon. As part of his training this week, he will run at least 41 kilometers and to avoid overtraining, at most 47 kilometers. He has already run 11 kilometers in training this week. Let x be the number of kilometers per 2 session he will run for the remaining training sessions this week. (Suppose he will decide to run the same distance each session.)

Question

(a)Find the possible numbers of kilometers per session Juan will run. Write your answer as a compound

Answer 1

inequality.

To find the possible numbers of kilometers per session, we need to consider the minimum and maximum number of kilometers Juan can run in total for the remaining training sessions.

Let x be the number of kilometers per session. Since there are two training sessions left, Juan will run 2x kilometers in total.

The minimum number of total kilometers Juan can run is 41 kilometers, so we have the inequality:
2x + 11 ≥ 41

Simplifying this inequality, we get:
2x ≥ 30
x ≥ 15

The maximum number of total kilometers Juan can run is 47 kilometers, so we have the inequality:
2x + 11 ≤ 47

Simplifying this inequality, we get:
2x ≤ 36
x ≤ 18

Combining these two inequalities, we get:
15 ≤ x ≤ 18

Therefore, the possible numbers of kilometers per session Juan will run are given by the compound inequality:
15 ≤ x ≤ 18.