Question

Carly is training for a triathlon. In her training routine each week, she runs 7 times as far as she swims, and bikes 3 times as far as she runs. One week she trained a total of 232. How far did she run that week?

Answer 1

Answer:
`56`

Explanation:

Let be "s" the distance Carly swam that week, "b" the distance Carly bikes and "r" the distance Carly ran that week.

According to the exercise:

`s+b+r=232` [Equation 1]

We know that she runs 7 times as far as she swims; then:

`r=7s` [Equation 2]

Since she bikes 3 times as far as she runs:

`b=3r` [Equation 3]

The steps to solve this are:

- Solve for "s" from the [Equation 2]:

`r=7s\\\\s=(r)/(7)`

- Substitute this into [Equation 1].

- Substitute [Equation 3] into [Equation 1].

Then:

`(r)/(7)+3r+r=232`

- Solve for "r":

`(r)/(7)+3r+r=232\\\\r((1)/(7)+3+1)=232\\\\(29)/(7)r=232\\\\r=(232)((7)/(29))\\\\r=56`