Question

Casandra is training for the 10 mile race. On the first day of training she runs 4 miles,each day after that she adds on 0.5 mile. On what day will Casandra run 8 miles?

Answer 1

Casandra will run 8 miles on the 9th Day.

Explanation:

Given:

Casandra on first day of training she runs 4 miles

So we can say that;

`a_1=4\ miles`

Also Given:

each day after that she adds on 0.5 mile.

So we can say that;

Common difference
`d=0.5\ miles`

We need to find on what day she will run 8 miles.

So we can say that;

`T_n = 8`

Let the number of the day be denoted by 'n'

Solution:

Now By using the formula of Arithmetic Progression we get;

`T_n= a_1+(n-1)d`

Now substituting the values we get;

`8=4+(n-1)0.5`

Now by using distributive property we get;

`8 =4+0.5n-0.5\\\\8=3.5+0.5n`

Now subtracting both side by 3.5 we get;

`8-3.5=3.5+0.5n-3.5\\\\4.5=0.5n`

Dividing both side by 0.5 we get;

`(4.5)/(0.5)=(0.5n)/(0.5)\\\\9=n`

Hence Casandra will run 8 miles on the 9th Day.