Question

Raven runs 12 miles throughout her first week of training and decreases her total distance by 1/10 of a mile each week after. Josh runs 2 miles during his first week of training and increases his total distance by 1/10 of a mile each week after. After how many weeks will Raven and Josh run the same amount?

Answer 1

It will take approximately 33.33 weeks for Raven and Josh to run the same amount.

Step-by-step explanation:

To find the number of weeks it takes for Raven and Josh to run the same amount, we need to set up an equation.

Let x be the number of weeks.

Raven's total distance after x weeks is given by 12 - (1/10)x.

Josh's total distance after x weeks is given by 2 + (1/10)x.

Setting these two expressions equal to each other, we have 12 - (1/10)x = 2 + (1/10)x.

Now, we can solve for x.

12 - (1/10)x = 2 + (1/10)x

10 = (2/10)x + (1/10)x

10 = (3/10)x

x = 10(10/3)

x = 100/3 = 33.33

Therefore, it will take approximately 33.33 weeks for Raven and Josh to run the same amount.