it takes 3/4 of an hour for an automated sprinkler to cover 2/7 of a lawn. after an hour has passed, what fraction of the lawn has been covered?
(2/7)/(3/4) * 1h = 2/7 * 4/3 * 1 =
To find the fraction of the lawn that has been covered after an hour, we need to determine how many times the automated sprinkler covers the lawn in an hour.
We know that it takes 3/4 of an hour for the sprinkler to cover 2/7 of the lawn. Let's first calculate how many times the sprinkler covers the lawn in an hour.
To cover 2/7 of the lawn, it takes 3/4 of an hour. Therefore, in 1 hour, the sprinkler will cover:
(1 hour) * (7/2) / (3/4) = (1 * 7 * 4) / (2 * 3) = 28/6 = 14/3 of the lawn.
Now, to find the fraction of the lawn covered after an hour, we divide the total lawn covered (14/3) by the whole lawn (1):
(14/3) / 1 = 14/3.
So, after an hour has passed, the fraction of the lawn covered is 14/3.