Q 8.168. Carrie can weed the garden in 7 ... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 8.168. (page 1006)

Carrie can weed the garden in 7 hours, while her mother can do it in 3. How long will it take the two of them working together?

Short Answer

Expert verified

In $2 hours and 6 minutes$ Carrie and her mother can weed the garden together.

Step by step solution

Step 1. Given information.

Carrie can weed the garden in 7 hours, while her mother can do it in 3.

Let's take $t =$ the number of hours needed to weed the garden together.

Step 2. Find the time needed to weed the garden together.

Organize the given information in a chart:

	Number of hours to weed the garden	Part of the garden weeded/ hour
Carrie	$7$	$\frac{1}{7}$
Her Mother	$3$	$\frac{1}{3}$
Together	$t$	$\frac{1}{t}$

Part of the Garden weeded by Carrie and her mother equals the amount completed together.

Carrie $+$ Her mother $=$ Together

role="math" localid="1648625695829" $\frac{1}{7} + \frac{1}{3} = \frac{1}{t}$

Multiply both sides by the LCD,

$21 t (\frac{1}{7} + \frac{1}{3}) = 21 t (\frac{1}{t})$

Simplify,

$3 t + 7 t = 21 10 t = 21 t = \frac{21}{10} \frac{21}{10} = 2 hours and 6 minutes$

Therefore, the total time taken by both Carrie and her mother to weed the garden together is $2 hours and 6 minutes$ .

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91影视

Carrie can weed the garden in 7 hours, while her mother can do it in 3. How long will it take the two of them working together?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the time needed to weed the garden together.

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