Question

If a sprinkler waters 1 over 12 of a lawn in 1 over 2 hour, how much time will it take to water the entire lawn?

Answer 1

A. 7/12

B. 1/6

C. 6

D. 10

Answer 2

I think it's 6 because flip 1/2 to 2/1 the 1 • 2 = 2 and 12 • 1 = 12 which would equal 2/12. I see that 2 and 12 remind me of 6 so 12 ÷ 2 = 6

Answer 3

Am I right?

Answer 4

There are a few ways to do this. one way is write a ratio
\[ \frac{ \frac{1}{12} \ lawn}{\frac{1}{2} \ hour}= \frac{1 \ lawn}{x \ hours} \]

Answer 5

the other way to think of it is as
rate * time = 1 lawn
rate is the amount of lawn watered divided by time
time is unknown, call it x
so you get
\[ \frac{ \frac{1}{12} \ lawn}{\frac{1}{2} \ hour} x=1 \]

Answer 6

in either case, you should simplify the messy fraction
\[ \frac{ \frac{1}{12} \ lawn}{\frac{1}{2} \ hour} \]
by mutliplying top and bottom by 2
\[ \frac{ \frac{1}{12} \cdot 2}{\frac{1}{2} \cdot 2} \]
1/2 * 2 is 1 so the fraction becomes
\[ \frac{ \frac{1}{12} \cdot 2}{1}= \frac{1}{12} \cdot 2 \]
and that becomes
\[ \frac{2}{12} = \frac{1}{6} \]

Answer 7

now you can solve for the time
1/6 * x = 1
multiply both sides by 6
you get
x=6 hours

or using ratios
\[ \frac{1}{6}= \frac{1}{x}\]
cross multiply to get
x=6