# It takes Cynthia 11 hours to proof a chapter of Hawkes Learning Systems Intermediate Algebra book and it takes Mandy 5 hours. How long would it take them working together?

Oct 27, 2017

Together it would take $3 \frac{7}{16}$ hours

#### Explanation:

Cynthia can proof (1" chapter")/(11" hours")=1/11 "chapters/hour"

Mandy can proof (1" chapter")/(5" hours")=1/5 "chapters/hour"

Together in one hour they could proof
$\frac{1}{11} \text{ chapters" +1/5" chapters"=(5+11)/55" chapters"=16/55" chapters}$

16/55 " chapters"/" hour"=(1" chapter")/(55/16" hours")=(1" chapter")/(3 7/16" hours")

Oct 27, 2017

$3 \frac{7}{16}$ hours

#### Explanation:

Cynthia took 11 hours to proof a chapter. So, in 1 hour she proofs 1/11 th part of that chapter.

Mandy took 5 hours to proof that chapter. So, in 1 hour he proof 1/5 th part of that chapter.

So, in 1 hour they proof together = $\frac{1}{11} + \frac{1}{5} = \frac{5 + 11}{55} = \frac{16}{55}$ th parts.

Total time taken by them to complete proofs the chapter
$\Rightarrow 1 \div \frac{16}{55} = 1. \frac{55}{16} = 3 \frac{7}{16}$hours.