Answer: 4 hours
Step-by-step explanation:
Shane: [tex]\dfrac{1}{4}\ \text{job per hour}[/tex]
Taylor: [tex]\dfrac{1}{x}\ \text{job per hour}[/tex]
Together: [tex]\dfrac{1}{2}\ \text{job per hour}[/tex]
Shane + Taylor = Together
[tex]\dfrac{1}{4}[/tex] + [tex]\dfrac{1}{x}[/tex] = [tex]\dfrac{1}{2}[/tex]
[tex](8x)\dfrac{1}{4}[/tex] + [tex](8x)\dfrac{1}{x}[/tex] = [tex](8x)\dfrac{1}{2}[/tex]
2x + 8 = 4x
8 = 2x
4 = x
