The statement "Lucy exercises for four days a week. Each session she warms up by walking for 15 minutes. She runs at a constant speed of 18 km per hour. She completes her workout with 15 minutes on the treadmill." is false.
To determine whether the statement "Lucy runs 76 km per week" is true, let's calculate the total distance Lucy runs each week.
Firstly, calculate the total time Lucy spends running each week:
Total running time = (Distance / Speed) * Time per day * Days per week
Total running time = (76 km / 18 km/hr) * 1 hour * 4 days
Total running time = 2.11 hours
Now, convert the total running time from hours to minutes:
Total running time in minutes = 2.11 hours * 60 minutes/hour
Total running time in minutes = 126.6 minutes
Since each session consists of 15 minutes of warming up and 15 minutes of cool-down on the treadmill, the total time spent on non-running activities is:
Total non-running time = 2 * 15 minutes/session * 4 days/week
Total non-running time = 120 minutes
Therefore, the total time Lucy spends exercising each week is:
Total exercise time = Total running time + Total non-running time
Total exercise time = 126.6 minutes + 120 minutes
Total exercise time = 246.6 minutes
Comparing the total exercise time to Lucy's four weekly exercise sessions, we can see that she spends an average of 61.65 minutes per session.
Since 61.65 minutes is greater than 60 minutes, it's impossible for Lucy to run 76 km per week. Therefore, the statement "Lucy runs 76 km per week" is false.