It makes 3/4 of an hour for an automated sprinkler to cover 2/7 of a lawn.After an hour has passed ,what fraction of a lawn has been covered
(3/4)/(2/7) = 1/x
(3/4)x = (2/7)
x = (2/7) / (3/4)
x = (2/7) * (4/3)
x = 8/21
To find out what fraction of the lawn is covered after an hour has passed, we need to determine how many times the sprinkler can cover the lawn in an hour.
Since the sprinkler covers 2/7 of the lawn in 3/4 of an hour, we can set up a proportion to find the coverage rate:
(2/7) / (3/4) = x / 1
To simplify, we multiply the numerator and denominator by the reciprocal of the fraction in the denominator:
(2/7) * (4/3) = x
8/21 = x
So, the fraction of the lawn covered by the sprinkler in an hour is 8/21.
To find out what fraction of the lawn has been covered after an hour, we need to determine how many times the automated sprinkler covers the lawn in an hour.
Since it takes 3/4 of an hour for the automated sprinkler to cover 2/7 of the lawn, we can set up a proportion to find the amount of time it takes to cover the whole lawn:
(3/4) hour = (2/7) lawn
Now, to find the fraction of the lawn covered in 1 hour, we can multiply both sides of the proportion by 4/3:
(3/4) hour * (4/3) = (2/7) lawn * (4/3)
This simplifies to:
1 hour = (8/21) lawn
Therefore, after an hour has passed, the automated sprinkler will cover 8/21 of the lawn.
1 hour is 4/3 as much as 3/4, so it will have covered 4/3 * 2/7 = 8/21 of the lawn.
or, using a ratio,
1/(3/4) = x/(2/7)