Mike can mow a lawn in 3 hours. Paul can mow the same lawn in 2 hours. How long would it take both of them working together to mow the lawn? The answer is suppose to be 20/9.
This is what I did and I get 9/20. What am i doing wrong?
1.4x+1/5x=1 which gives u 9/20. I'm so lost...
Mike's rate = 1/3 lawn/hr
Paul's rate = 1/2 lawn/h
combined rate = (1/3 + 1/2) lawn/hr
= 5/6 lawn/hr
time for combined rate = 1/(5/6) hours
= 6/5 hours
Their answer is wrong.
How can it take 20/9 or more than 2 hours for both of them to do it, when Paul alone could do it in 2 hours.
6/5hrs
t = 3*2 / (3+2) = 6/5 hrs.
To solve this problem, we can use the formula for the rate of work. The rate of work is the reciprocal of the time it takes to complete a task.
Let's denote the time it takes for Mike to mow the lawn as M hours, and the time it takes for Paul to mow the lawn as P hours. We are given that M = 3 hours and P = 2 hours.
Now, let's calculate the rates of work for each person:
Mike's rate of work = 1 lawn / 3 hours = 1/3 lawns per hour.
Paul's rate of work = 1 lawn / 2 hours = 1/2 lawns per hour.
To find the combined rate when they work together, we can add their rates:
Combined rate = Mike's rate + Paul's rate
= 1/3 lawns per hour + 1/2 lawns per hour
= (2 + 3) / 6 lawns per hour
= 5/6 lawns per hour.
Now we can use the formula for work, which states that work = rate * time, to solve for the time it takes for both of them to mow the lawn.
We know the combined rate is 5/6 lawns per hour. Let's denote the time it takes for both of them to mow the lawn as T hours. And we know that the work they do together is 1 lawn.
So, the equation is:
(5/6) * T = 1.
To solve for T, multiply both sides of the equation by 6/5:
T = (6/5) * 1
T = 6/5
T = 1.2
So, it would take both of them working together 1.2 hours (equivalent to 1 hour and 12 minutes) to mow the lawn.
The answer given in the question, 20/9, seems to be incorrect.