Algebra homework help

Question

Joe runs 7 miles per week and runs a mile each week after the first. Alex runs 4 miles per week and 2 miles every week after the first. In how many weeks will both be running the same distance, and what will that distance be? 

Answer 1

If I can add on to this, Katarina's approach is valid (although Alex starts at 4miles/week, so the solution is incorrect), but if you'd like an algebraic approach, let x=weeks. We want to find the week when the amount of miles that Alex runs equates the amount of miles that Joe runs, so:

Joe's miles = Alex's miles

Joe's miles = 7 + (7+1x), with 7 being his base miles, and (7+1x) being the miles he runs in a given week following that first week (x). X is multiplied by 1 because he only adds 1 mile for each subsequent week.

Alex's miles = 4+(4+2x), with 4 being his base miles, and(4+2x) being the miles he runs in a given week following the first week (x). The parentheses are not necessary in these expressions but they help to separate the variables and what they mean.

This gives 14+x = 8 + 2x --> 2x-x=14-8 --> x=6. Thus it is the sixth week when they run the same distance. You can test this using the "add up" method mentioned by Katarina.

Answer 2

For this problem, you want to find when the mileage for each person is the same. For this, I would add each week by week until you find they are equal.

Week 2- Joe 8, Alex 6

Week 3- Joe-9, Alex- 8

Week 4- Joe 10, Alex 10

So, your answer would be week 4