Final answer:
Mel needs to mow the remaining 2/3 of the yard after Michael mows 1/3. Since she can mow 3/4 of the yard in one hour, Mel will take 8/9 hours (or approximately 53 minutes and 20 seconds) to finish mowing her portion.
Step-by-step explanation:
The question asks about the time it will take Mel to finish mowing her part of the yard after Michael has mowed 1/3 of it. Since Mel can mow 3/4 of the yard in one hour, and Michael has already mowed 1/3, we need to calculate the remaining fraction of the yard that Mel needs to mow. To find this, let's figure out the fraction of the yard that is left after Michael's turn:
- Total yard = 1 (when representing the whole)
- Michael mows = 1/3 of the yard
- Remaining yard = 1 - 1/3
- Remaining yard = 3/3 - 1/3
- Remaining yard = 2/3
Mel needs to mow 2/3 of the yard. Since Mel can mow 3/4 of the yard in one hour, this is more than enough to mow the remaining 2/3, meaning she will need less than an hour. To find out exactly how long it will take Mel to mow 2/3 of the yard, we set up a proportion based on Mel's mowing rate:
(3/4 yard / 1 hour) = (2/3 yard / x hours)
Solving for x gives us the time Mel needs to finish mowing her part of the yard:
- (3/4) / (2/3) = 1 / x
- (3/4) * (3/2) = 1 / x
- 9/8 = 1 / x
- x = 8/9 hours
Therefore, it will take Mel 8/9 hours, or approximately 53 minutes and 20 seconds to finish mowing her part of the yard.