it would take 12 hours for her associate to complete the route by herself
Further explanation
This problem is related to the speed of completing the route.
To solve this problem, we must state the formula for the speed.
[tex]\large {\boxed {v = \frac{x}{t}} }[/tex]
where:
v = speed of completing the route ( m³ / s )
x = route distance ( m³ )
t = time taken ( s )
Let's tackle the problem!
Allison can complete a sales route by herself in 6 hours.
[tex]\text{Allison Speed} = v_a = x \div t_a[/tex]
[tex]v_a = x \div 6[/tex]
Her associate can complete the route by herself in t_s
[tex]\text{Associate Speed} = v_s = x \div t_s[/tex]
[tex]v_s = x \div t_s[/tex]
Working with an associate, she completes the route in 4 hours
[tex]\text{Total Speed} = v = v_a + v_s[/tex]
[tex]\frac{x}{t} = \frac{x}{t_a} + \frac{x}{t_s}[/tex]
[tex]\frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_s}[/tex]
[tex]\frac{1}{4} = \frac{1}{6} + \frac{1}{t_s}[/tex]
[tex]t_s = \frac{ 6 \times 4 }{6 - 4}[/tex]
[tex]t_s = \frac{ 24 }{2}[/tex]
[tex]t_s = 12 ~ \text{hours}[/tex]
Learn more
- Infinite Number of Solutions : https://brainly.com/question/5450548
- System of Equations : https://brainly.com/question/1995493
- System of Linear equations : https://brainly.com/question/3291576
Answer details
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
