john runs .5 miles per day. if he increases .5 miles a day, how many days until he reaches 7.5 miles?
.5 + .5d = 7.5
Solve for d.
.5 , 1 , 1.5 , 2.0 , 2.5
is
.5 , 1.5 3.0 , 5.0, 7.5 on day 5
of course this is an arithmetic sequence with d = .5
http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
a + (n-1)d
.5 + (n-1).5
To find out how many days it will take for John to reach 7.5 miles, we need to divide the total distance by the distance he increases per day.
John currently runs 0.5 miles per day, and he wants to increase it by 0.5 miles each day until he reaches 7.5 miles.
Let's set up an equation:
0.5 miles/day * X days = 7.5 miles
Here, X represents the number of days it will take.
We need to isolate X to find the answer. To do that, we'll divide both sides of the equation by 0.5 miles/day:
X = 7.5 miles / 0.5 miles/day
Simplifying this, we get:
X = 15 days
Therefore, it will take John 15 days to reach a total distance of 7.5 miles if he increases his daily run by 0.5 miles.