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

Question

3 years ago

15

g would it take her associate to complete the route by herself?

2 answers:

iogann1982 [59] · Answer 1 · 2022-05-06T10:16:54+03:00

6 0

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:

statuscvo [17] · Answer 2 · 2022-05-06T12:42:11+03:00

it would take 12 hours for her associate to complete the route by herself

<h3>Further explanation</h3>

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:

<em>v = speed of completing the route ( m³ / s )</em>

<em>x = route distance ( m³ )</em>

<em>t = time taken ( s )</em>

Let's tackle the problem!

<em>Allison can complete a sales route by herself in 6 hours.</em>

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

$v_a = x \div 6$

<em>Her associate can complete the route by herself in t_s</em>

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

$v_s = x \div t_s$

<em>Working with an associate, she completes the route in 4 hours</em>

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

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

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

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

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

$t_s = \frac{ 24 }{2}$

$t_s = 12 ~ \text{hours}$

<h3>Learn more</h3>

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

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