Question

Hugo begins a walking program by walking 1/2 r mile per day for one week. each week thereafter he increases his mileage by 10%. how many weeks will it take him to walk at least 5 miles a day?

Answer 1

To determine how many weeks it will take Hugo to walk at least 5 miles a day, we can set up an equation and solve for the number of weeks. Using the given values for r and solving for n, we can find how many weeks it will take Hugo to walk at least 5 miles a day.

Step-by-step explanation:

To determine how many weeks it will take Hugo to walk at least 5 miles a day, we can set up an equation and solve for the number of weeks.

The equation can be set up as follows:

1/2 r + 1.1 * (1/2 r) + 1.1^2 * (1/2 r) + ... + 1.1^n * (1/2 r) >= 5

Where n represents the number of weeks it takes.

To solve for n, we can use logarithms:

log(1/2 r) + log(1.1^n) >= log(5)

n log(1.1) >= log(5) - log(1/2 r)

n >= (log(5) - log(1/2 r)) / log(1.1)

Using the given values for r and solving for n, we can find how many weeks it will take Hugo to walk at least 5 miles a day.