Question

Gymnasts training for an upcoming competition are practicing their routines for balance beam and floor exercise. During morning practice, Rosanne practiced her beam routine 1 time and her floor routine 1 time, which took a total of 3 minutes. During afternoon practice, she ran through her her beam routine 4 times and her floor routine 6 times, which took a total of 14 minutes. How long is each routine? The beam routine is minutes long and the floor exercise is minutes long.

Answer 1

Answer:

The beam routine is two (2) minutes long and the floor exercise is one (1) minute long.​

Step-by-step explanation:

Let Rosanne's beam routine be represented by x, and the floor routine be represented by y.

Since it took her 3 minutes to complete one of the beam and floor routines, we have:

`x+y=3...............................................(1)`

During her afternoon practice, she ran through her beam routine 4 times and her floor routine 6 times, which took a total of 14 minutes

`4x+6y=14.................................................(2)`

(2) may be written as:

`2x+3y=7...............................................(3)`

To know how long each routine is, we solve (1) and (3) simultaneously as follows.

Subtract twice equation (1) from equation (3)

`\begin{gathered} 2x-2x+3y-2y=7-6 \\ y=1 \end{gathered}`

Substitute y = 1 into equation (1)

`\begin{gathered} x+1=3 \\ x=3-1=2 \end{gathered}`

The beam routine, x = 2 minutes long

The floor exercise, y = 1 minute long.​