Working together, two people can mow the lawn in 24 minutes. Working alone, one person takes 20 minutes longer than the other. How many minutes would it take each person to mow the lawn alone?
Thanks!!!
1/24 = 1/x + 1/(x+20)
x = 40
1st person: X min.
2nd person: (X+20) min.
X*(X+20)/(X+X+20) = 24 min.
(X^2+20X)/(2X+20) = 24
X^2+20X = 48X+480
X^2-28X-480 = 0
Use Quadratic formula and get:
X = 40 min.
X+20 = 60 min.
60
To find the time it takes each person to mow the lawn alone, let's assign variables to represent their individual mowing rates.
Let's say the first person's mowing rate is represented by "x" lawns per minute, and the second person's mowing rate is represented by "y" lawns per minute.
We know that when they work together, they can mow the lawn in 24 minutes. This means that their combined mowing rate is 1 lawn per 24 minutes. Thus, we can set up the equation:
(x + y) * 24 = 1
Next, we know that when each person works alone, one person takes 20 minutes longer than the other. Therefore, their individual mowing times are x and x + 20.
To find their individual mowing rates, we can set up two equations using the formula "rate * time = work":
x * (x + 20) = 1
y * x = 1
From here, we have a system of two equations with two variables. We can solve this system to find the values of x and y, which represent the mowing times for each person alone.