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problem solving.
10. Nathan decides to exercise each week by jogging. He starts in week 1 by jogging for 20mins. In week 2 he jogs for 30 mins. in week 3 he jogs for 40 mins. and so on. He keeps a record of the total times he spends jogging. After how many weeks is his total 18290mins.
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Re: problem solving.
Arithmetic series, a = 20, d = 10, Sn = 18290
Sn = (n/2)[2a + (n - 1)d]
18290 = (n/2)[40 + 10(n - 1)]
18290 = n[20 + 5(n - 1)]
18290 = n[20 + 5n - 5]
18290 = n[5n + 15]
18290 = 5n2 + 15n
0 = 5n2 + 15n - 18290
0 = n2 + 3n - 3658
Solve quadratic and take positive answer for n (the number of weeks)
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Re: problem solving.
ok but is there a way to work it up without using arithematic series? Because we havent learned it yet.
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Re: problem solving.
He starts at 20 and ends at 18290, an increase of 18270.
He does this at a rate 10 per week and the number of weeks is increase/rate.