Question

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

Answer 1

`6 " hours"`

Explanation:

Since `72=6xx12`

If
`color(white)("XXX")12 " math problems"` take `1 " hour"`
then
`color(white)("XXX")6xx12 " math problems "` take `6xx1 " hours"`

i.e.
`color(white)("XXX")72 " math problems "` take `6 " hours"`

Answer 2

Let's make proportion.

1 hour for 12 problems
x hours for 72 problems

x = 72/12 = 6

Answer 3

`x=6" hours"`

Explanation:

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

`("time taken")/("work done")`

So the initial condition is: `1/12`

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

`1/12=x/72`

Then multiply both sides by 72:

`x=72xx1/12`

`x=6`

`color(brown)("Don't forget the units! This little thing will get you more marks!!")`

`x=6" hours"`