Need Help with word problem for middle school!?

Question

megan runs 2 miles each day,5 days a week. she wants to run a marathon, so she asked her coach for some advice.

the coach told megan that she needs to work herself up to a training routine of 40 miles each week and that she rbe running that much for at least 6 weeks prior to the marathon. in addition the coach told megan that she should not increase her mileage by more than 10% every 2 weeks.

if megan follows her coaches advice in how many weeks can she enter her first marathon.

show ur work n explain how u arrived at ur answer.

Answer 1

megan runs 10 miles a week now

increase 10% every 2 weeks ..1 mile first 2 weeks

ahh ..h**l

too much work to show for ten pts..

32 weeks ..

Answer 2

If Megan increases her distance by 10% every two weeks, then she increases it by 5% every week.  We can use an exponential growth formula to express the progressive increase until she reaches 40 miles per week this way:

D = d (1.05)^n, where D is the ending distance, d is the starting distance, and n is the number of weeks it takes to reach D.

Plug in the appropriate values for D, and d.  Then divide through by d, and then use logarithms to solve for n (all logs are in base 10):

D/d = (1.05)^n

log (D/d) = n log (1.05)

40 = 10 (1.05)^n

40/10 = (1.05)^n

4 = (1.05)^n

log 4 ≈ n log (1.05)

0.6021 ≈ n (0.0212)

(0.6021)/(0.0212) ≈ n

28.4 ≈ n

So it will take Megan about 28.4 weeks to reach her final running distance of 40 miles per week.  Then we add on an additional 6 weeks.  So the total time until Megan can run a marathon is about 28.4 + 6, or about 34.4 weeks.

We can verify that this solution will work by plugging our calculated value for n back into the original equation:

D = d (1.05)^n

40 ≈ 10 (1.05)^28.4

40 ≈ 10 (3.997)

40 ≈ 39.97

The equation closely balances, so our calculated value for n is close enough to the true value.

Answer 3

current mileage = 2*5 = 10 miles per week

You can either keep adding 10% to that until you get to 40, or use a compound interest calculation to figure out how many increases she will have to make.

http://en.wikipedia.org/wiki/Compound_in...

Divide the number of increases by 2, since she is only to increase it every 2 weeks, and add 6 weeks, then you'll have the total.

Answer 4

Do some thinking here.  How many miles a week is she running now?  5% of that (10% every two weeks is 5% a week) is how much?  How much would she be running the second week? and the third?  and so on.  You can figure it out if you break it down.