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
This is just a way to convert hours to lawns
1 hr * (2/7 lawn)/(3/4 hr) = 2/7 * 4/3 = 8/21 lawn
To find the fraction of a lawn that has been covered after an hour has passed, we need to determine how many times the automated sprinkler can cover 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 break it down step by step:
1. 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 calculate:
(7/2) / (3/4) = (7/2) * (4/3) = 14/3
So, the sprinkler can cover the lawn (14/3) times in an hour.
2. Calculate the fraction of the lawn covered after one hour:
Since the sprinkler can cover the lawn (14/3) times in an hour, we need to multiply that by the fraction of the lawn it covers each time:
(14/3) * (2/7) = (14 * 2) / (3 * 7) = 28/21 = 4/3
Hence, after one hour has passed, the fraction of the lawn covered is 4/3.
Therefore, the fraction of the lawn covered after an hour is 4/3.