SOLUTION: Miku and John began biking from the same place on the same road, heading in the same direction. Each day, Miku bikes 25 miles. John bikes 5 miles the first day, 8 miles the second

Question 167753: Miku and John began biking from the same place on the same road, heading in the same direction. Each day, Miku bikes 25 miles. John bikes 5 miles the first day, 8 miles the second day and so on. Each day, biking three more miles than he biked the previous day. If they began on July 1, on waht date did John passed Miku?
I got the answer with a table but i dont know how to show it into algebraic equation.
How do you change John's pattern into an equation?
5,13,24,38,56,76,99,125...........
My work so far:
Miku= 25x x = days
John= 5+(5+3)+(5+3+3)+(5+3+3+3).....
5x+???= nth term

so far, the only part of the equation ive figured out is the 5x....
though i think that there should be a disributive property in the equation.
Im really confused and have been working this problem for hours.
I really need help.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the sum of the terms for an arithmetic sequence is the number of terms (n) multiplied by the average value of the terms
__ (T1+Tn)/2

S = n(5+5+3(n-1))/2 = n(10+3n-3)/2 = (3n^2+7n)/2

(3n^2+7n)/2 = 25n __ 3n^2+7n=50n __ 3n^2-43n=0 __ n(3n-43)=0

n=0 __ they are together on July 1

3n-43=0 __ 3n=43 __ n=14 1/3 __ John passed Miku on July 15
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