Allison can complete a sales route by herself in 6 hours. Working with an associate, she completes the route in 4 hours. How long would it t

Question

Allison can complete a sales route by herself in 6 hours. Working with an associate, she completes the route in 4 hours. How long would it take her associate to complete the route by herself?

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Ayla 2 weeks 2021-10-12T11:38:20+00:00 2 Answers 0

Answers ( )

    0
    2021-10-12T11:40:03+00:00

    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.

    \large {\boxed {v = \frac{x}{t}} }

    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.

    \text{Allison Speed} = v_a = x \div t_a

    v_a = x \div 6

    Her associate can complete the route by herself in t_s

    \text{Associate Speed} = v_s = x \div t_s

    v_s = x \div t_s

    Working with an associate, she completes the route in 4 hours

    \text{Total Speed} = v = v_a + v_s

    \frac{x}{t} = \frac{x}{t_a} + \frac{x}{t_s}

    \frac{1}{t} = \frac{1}{t_a} + \frac{1}{t_s}

    \frac{1}{4} = \frac{1}{6} + \frac{1}{t_s}

    t_s = \frac{ 6 \times 4 }{6 - 4}

    t_s = \frac{ 24 }{2}

    t_s = 12 ~ \text{hours}

    Learn more

    Answer details

    Grade: High School

    Subject: Mathematics

    Chapter: Linear Equations

    Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

    0
    2021-10-12T11:40:15+00:00

    Answer:

    So, Allison averages 1/6 of the route every hour, right?

     

    1/6 + 1/a = 1/4

     

    Once we apply the common denominator, 12a, we only wirk with the numerators.

     

    2a + 12 = 3a

    a = 12

     

    Her associate can finish the route in 12 hours by herself.

    Step-by-step explanation:

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