John can cut the grass in 4 hours working by himself. When john cuts the grass with his younger brother michael, it takes 3 hours. How long would it take michael to cut the grass by himself?
John's rate = 1/4
Michael's rate = 1/x
combined rate = 1/4 + 1/x = (x+4)/(4x)
given:
1/( (x+4)/(4x) ) = 3
4x/(x+4) = 3
4x = 3x + 12
x = 12
Michael alone would take 12 hours
check:
combined rate = 1/4 + 1/12 = 1/3
time at combined rate = 1/(1/3) = 3
To find out how long it would take Michael to cut the grass by himself, we can use the concept of work rates.
Let's assume that John's work rate is represented by J (in units of grass area per hour) and Michael's work rate is represented by M (also in units of grass area per hour).
From the given information, we know that John can cut the grass in 4 hours working alone. So, we can say his work rate is 1/4 of the total grass area per hour (since he completes the entire task in 4 hours).
Working together, John and Michael can complete the task in 3 hours. So, their combined work rate is 1/3 of the total grass area per hour (since they complete the entire task in 3 hours).
To find out how long it would take Michael to cut the grass by himself, we need to determine his individual work rate (M). We can do that by subtracting John's work rate (J) from the combined work rate of John and Michael.
M = (John and Michael's combined work rate) - J
M = 1/3 - 1/4
M = (4/12) - (3/12)
M = 1/12
Therefore, Michael's work rate is 1/12 of the total grass area per hour. This means it would take him 12 hours to cut the grass by himself, as his work rate is lower than John's.