# How solve it?

## Camila begins to exercise in a new gym where the coach explains that the work consisted in 5 minutes of warm-up 25 trot and 15 days in the eliptca machine .... at the end of each week of training should increase 3 minutes of jogging and 5 of elliptical machine in how many weeks will the trotting time be equal to the time that camila uses the elliptical machine? A) 5 B) 4 C) 6 D) 7 THANK YOU

Jun 3, 2017

After 5 weeks.

#### Explanation:

I'm assuming that the elliptical workout time is 15 mins and not 15 days (cause that's a looong time).
You need to set up two equations. They will be of the form, time of each workout (t) as a function of number of weeks (x).

The trotting time starts off as 25 mins, then increases by 3 mins per week. In other words, 25 + 3 times the number of weeks. So the equation looks like this:

${t}_{\text{trot}} \left(x\right) = 3 x + 25$

In the same way, the time of the elliptical machine is 15 mins plus 5 mins per week:

${t}_{\text{elliptical}} \left(x\right) = 5 x + 15$

To solve for $x$, set the times equal to each other:

${t}_{\text{trot"(x)=t_"elliptical}} \left(x\right)$

Then solve for $x$:

$3 x + 25 = 5 x + 15$

$25 - 15 = 5 x - 3 x$

$10 = 2 x$

x=?

The workout time will be given by substituting the answer for $x$ into each equation.
You can see the answer by graphing the two straight lines and seeing where they intersect (5,40):