After 4 interval of six months, Joe to earn same hourly rate as Blaine
<em><u>Solution:</u></em>
Given that,
Amount earned by Joe = $ 14 per hour
Amount earned by Blaine = $ 18 per hour
Lets assume the number of six month intervals be "x"
<em><u>Joe receives a raise of $1.75 every six months</u></em>
Therefore,
Joe earning: 14 + 1.75(number of six month intervals)
Equation for Joe earning: 14 + 1.75x ------- eqn 1
<em><u>Blaine receives a raise of $0.75 every six months</u></em>
Therefore,
Blaine earning: 18 + 0.75(number of six month intervals)
Equation for Blaine earning: 18 + 0.75x ------------ eqn 2
The number of six-month intervals it will take Joe to earn the same hourly rate as Blaine,
Eqn 1 must be equal to eqn 2
![14+1.75x = 18+0.75x\\\\1.75x-0.75x = 18-14\\\\1x = 4\\\\x = 4](https://tex.z-dn.net/?f=14%2B1.75x%20%3D%2018%2B0.75x%5C%5C%5C%5C1.75x-0.75x%20%3D%2018-14%5C%5C%5C%5C1x%20%3D%204%5C%5C%5C%5Cx%20%3D%204)
Thus after 4 interval of six months, Joe to earn same hourly rate as Blaine.