Man! How do you figure out the equation for this thing?!?

Question

After 6 weeks on a fitness program, Greg jogs 35 miles per week. His average mileage gain has been 2 miles per week.

Write and equation that models Greg's weekly mileage (m) in terms of the number of weeks (n) that he stays on the program.

Answer 1

Roman please! Don't confuse the poor girl any more than she already is. Which is it, 23 or 24?

Tat, Roman was on the right track with this one. He had the right concept, but the wrong constant in the end. Guess that's why the Caesars no longer rule.

If Greg now runs 35 miles today, then six weeks ago he started running 35 - 2(6) or 23 miles per week. Letting m be the mileage run per week, and n the number of weeks he runs, then we come up with this equation for the mileage Greg runs each week he is on the program.:

m = 23 + 2n.

We defy the normal convention of putting the constant at the end of the equation this time, because that was the mileage Greg started with, and everything else is added to it.

Answer 2

Since Greg has been in the program (P) for six weeks, and his average gain (AG) is 2 miles per week, and his current rate (CR) is 35 miles, he has gained 12 miles over his starting rate. His starting rate could also be called the baseline (B) You must know the baseline to compute future rates (FR) So...
B=CR-(P*AG)
B=35- (6 * 2)
B=27

The future rate will depend on how many weeks he spends in the program (n) added to the baseline. So... the formula is:
FR=B + (n * AG)

Assuming that he stays in the program another 10 weeks, he will be in the program a total of 16 weeks, and plugging those numbers into the formula, we get the following:

FR = 27 + (16 * 2)
FR = 27 + 32
Fr= 59

Of course we don't know the speed that he is moving, so we don't know how much time is being spent jogging. At some point in the program he will be using all available time jogging, so further gains are impossible... but that's beyond the scope of this simple problem.i

Answer 3

If Greg ran for 6 weeks and gains 2 miles per week, that means he started out 12 miles shorter then 35. So we start with 23.

Beyond that it's a simple algebra equation:

Milage = 2 * Number of Weeks + 23
M = 2N + 23

If you are starting the equation from the 6 week period and not from the beginning, you would use M = 2N + 35 instead.

Answer 4

I'll start you off. Let's work backwards: his mileage has increased 2 miles a week for 6 weeks, which comes to 12 miles, so his starting point was 35 - 12 miles, or 23 miles. So when n = 0, m = 23. That makes 23 the y-intercept (or in this case, the m-intercept) You take it from there.

Answer 5

When n = 6, m = 35 and you can see that when n = 5, m was 33

So slope = (35-33)/(5-4) = 2

m = 2n + b

35 = 12 + b

b = 23

So, m = 2n + 23

Answer 6

ok...well if he jogs 35 miles per week and he increases 2mi each week...let n be teh number of weeks in teh program

so m [the mileage]= 35 [initial amount per week] + 2n

m=35+2n

hope this helps

matttlocke