# Megan finished 12 math problems in one hour. At this rate, how many hours will take her to complete 72 problems?

Feb 1, 2016

$6 \text{ hours}$

#### Explanation:

Since $72 = 6 \times 12$

If
color(white)("XXX")12 " math problems" take $1 \text{ hour}$
then
color(white)("XXX")6xx12 " math problems " take $6 \times 1 \text{ hours}$

i.e.
color(white)("XXX")72 " math problems " take $6 \text{ hours}$

Feb 1, 2016

Let's make proportion.

1 hour for 12 problems
x hours for 72 problems

x = 72/12 = 6

Feb 1, 2016

$x = 6 \text{ hours}$

#### Explanation:

How ever you choose to approach this, you will find that they are all based on this ratio fact:

$\left(\text{time taken")/("work done}\right)$

So the initial condition is: $\frac{1}{12}$

This is presumed to be constant so,
let the unknown time (hours) be $x$:

$\frac{1}{12} = \frac{x}{72}$

Then multiply both sides by 72:

$x = 72 \times \frac{1}{12}$

$x = 6$

$\textcolor{b r o w n}{\text{Don't forget the units! This little thing will get you more marks!!}}$

$x = 6 \text{ hours}$