Problem

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Problem 46 Hard Difficulty

Solve each problem.
Constantin Arne has started on a fitness program. He plans to jog 10 min per day for the first week and then add 10 min per day each week until he is jogging an hour each day. In which week will this occur? What is the total number of minutes he will run during the first four weeks?

Answer

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Precalculus

Beginning and Intermediate Algebra

Chapter 14

Sequences and Series

Section 2

Arithmetic Sequences

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Video Transcript

So in this problem, we're told Constantine is going to start a new fitness program. So initially we were told that he's going to jog 10 minutes per day for the first week. Then he's going to add 10 minutes per day for each week, up until he's jogging hour a day. We want to know in which weak Will he jog one outward? Well, let's think about it. He's gonna jog 10 minutes each day during the first week. Then we're gonna increase that by 10 minutes. That means it'll be 20 minutes during the second week, 30 during the third 40 during the fourth 50 during the fifth and 60 during the six, while 60 minutes is an hour. While how many weeks did it take us? It took us 123456 weeks. So the answer, the first part. Which week will he jog one hour a day in the six week? Actually, you know what? I'm going to type this out because I think it's gonna be faster for myself. So in the six week, you will be jogging one hour a day. So that's the answer to our first question. So it's going to take him six weeks before he's going to jog that one hour a day. All right, well, let's go to that second question here. We're being asked, what is the total number of minutes he will run during the first four weeks? Well, let's think about the total he's gonna run during the first week. He's jogging 10 minutes a day and there seven days in the week. So 10 times seven will be the total number of minutes he runs during the first week, which is 70 now. Remember, in the second week, we already found he's gonna be jogging for 20 minutes. So the find the total will do 20 times seven, which is 140 for the third week. Same process 30 times seven, which is 210. And for the fourth week, 40 times seven, which is equal to 280. So now all we need to dio is out of these values to find the total So 70 plus 100 40 plus 210 back that up. So looks pleasurable here, plus two on your 80. So now we just like I said, I need to add these together, so 70 plus 1 40 is equal to two ton plus two. Tennis for 20 plus 2 80 is equal to 700. So that means during the first four weeks he would run 700 minutes. So again, I'm going to type this out. Can I think you'll be factor? So he will run 700 minutes during the first four weeks. So again, you could have used, um, sequence and Siri's information to do this. But sometimes it can be easier just to do it out like you normally would.

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