Question

Recommendations2 Skill plansMathL Language artsScienceSocial studiesHTX StandAlgebra 1U.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveall GolWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.There are two trails near Joel's house that he runs regularly, a short loop and a long loop.Last week, he ran 3 short loops and 4 long loops, for a total of 30 miles. This week, he ran 2short loops and 6 long loops, covering a total of 40 miles. What is the length of each loop?The short loop has a length ofmiles.miles, and the long loop has a length ofSubmit

Answer 1

Let:

x = Length of the short loop

y = Length of the long loop

Joel ran 3 short loops and 4 long loops, the total distance was 30mi, so:

`3x+4y=30_{\text{ }}(1)`

He also ran 2 short loops and 6 long loops, the total distance was 40mi, so:

`2x+6y=40_{\text{ }}(2)`

From (1) solve for x:

`\begin{gathered} 3x=30-4y \\ x=10-(4)/(3)y_{\text{ }}(3) \end{gathered}`

Replace (3) into (2):

`\begin{gathered} 2(10-(4)/(3)y)+6y=40 \\ 20-(8)/(3)y+6y=40 \\ (10)/(3)y=20 \\ y=(60)/(10) \\ y=6 \end{gathered}`

Replace y into (3):

`\begin{gathered} x=10-(4)/(3)(6) \\ x=2 \end{gathered}`

Answer:

The short loop has a length of 2 miles

The long loop has a length of 6 miles