Question

on monday, carly walked 3 miles and ran 2 miles for a total of 78 minites on a treadmill. on thursday she walked 2 miles and ran 3 miles for atotal of 72 minutes using the same speed setting for the treadmill as she did on Monday. let wand r represent the rates, in minutes per mile , that carly walked a d ran on the treadmill, respectivelsy​

Answer 1

w=18 minutes per mile, r=12 minutes per mile

Explanation:

Let w and r represent the rates, in minutes per mile, that Carly walked and ran on the treadmill, respectively.

1. On Monday, Carly walked 3 miles and spent 3w minutes, ran 2 miles and spent 2r minutes. In total Carly spent 78 minutes, so

3w+2r=78

2. On Thursday, Carly walked 2 miles and spent 2w minutes, ran 3 miles and spent 3r minutes. In total Carly spent 72 minutes, so

2w+3r=72

Solve the system of two equations:

`\left \{ {{3w+2r=78} \atop {2w+3r=72}} \right.`

Multiply the first equation by 2, the second equation by 3 and subtract them:

`2(3w+2r)-3(2w+3r)=2\cdot 78-3\cdot 72\\ \\6w+4r-6w-9r=156-216\\ \\-5r=-60\\ \\r=12`

Substitute it into the first equation:

`3w+2\cdot 12=78\\ \\3w=78-24\\ \\3w=54\\ \\w=18`