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

3 Answers

Feb 1, 2016

$6 hours$ $6 " hours"$

Explanation:

Since $72 = 6 \times 12$ $72=6xx12$

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

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

Feb 1, 2016

Let's make proportion.

1 hour for 12 problems
x hours for 72 problems

x = 72/12 = 6

Tony B · Alan P.

Feb 1, 2016

$x = 6 hours$ $x=6" hours"$

Explanation:

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

$\frac{time taken}{work done}$ $("time taken")/("work done")$

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

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

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

Then multiply both sides by 72:

$x = 72 \times \frac{1}{12}$ $x=72xx1/12$

$x = 6$ $x=6$

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

$x = 6 hours$ $x=6" hours"$

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