When all the leaves have fallen a girl can rake the entire yard in 4 hours. When a boy does italone,it takes him 9 hours. How long would it take them to rake the yard together? Round to the nearest minute
When all the leaves have fallen, a girl can rake the entire yard in 4 hours. When a boy does it alone, it takes him 10 hours. How long would it take them to rake the yard together? Round to the nearest minute.
To find out how long it would take them to rake the yard together, we can use the formula:
1 / (x) + 1 / (y) = 1 / (z)
Where:
x = the time it takes for the girl to rake the yard alone (4 hours)
y = the time it takes for the boy to rake the yard alone (9 hours)
z = the time it takes for them to rake the yard together (unknown)
Replacing the values in the equation:
1 / (4) + 1 / (9) = 1 / (z)
Simplifying the equation:
9z + 4z = 36
13z = 36
To solve for z, divide both sides of the equation by 13:
z = 36 / 13
Rounding to the nearest minute:
z ≈ 2.77 hours
Converting hours to minutes:
2.77 hours ≈ 2 hours and 46.2 minutes
Rounding to the nearest minute:
z ≈ 2 hours and 46 minutes
Therefore, it would take them approximately 2 hours and 46 minutes to rake the yard together.
To find out how long it would take them to rake the yard together, we can use the concept of "work rates."
Let's assume that the total work required to rake the yard is represented by the unit "1."
First, we need to determine the individual work rates of the girl and the boy. We can calculate this by considering the time it takes each person to complete the job independently.
For the girl:
If it takes her 4 hours to complete the entire yard, her work rate would be 1 yard / 4 hours = 1/4 yard per hour.
For the boy:
If it takes him 9 hours to complete the entire yard, his work rate would be 1 yard / 9 hours = 1/9 yard per hour.
Now, we can add their work rates together to find their combined work rate when working together:
Combined work rate = girl's work rate + boy's work rate
Combined work rate = 1/4 yard per hour + 1/9 yard per hour
To add these fractions together, we need a common denominator. In this case, the least common multiple (LCM) is 36.
Combined work rate = (1/4) * (9/9) yard per hour + (1/9) * (4/4) yard per hour
Combined work rate = 9/36 yard per hour + 4/36 yard per hour
Combined work rate = 13/36 yard per hour
Now, we can find out how long it would take them to complete the work together. Since the work rate is in yards per hour, we'll set up a ratio to solve for the time:
13/36 yard per hour = 1 yard / x hours
To solve the equation for x (the time it takes to rake the yard together), we can cross multiply:
13x = 36
x = 36/13
Now, we can use a calculator to divide and get the decimal value:
x ≈ 2.77 hours
To convert this to minutes, we'll multiply by 60:
2.77 hours * 60 minutes/hour ≈ 166.2 minutes
Rounding this value to the nearest minute, we get approximately 166 minutes.
Therefore, it would take them approximately 166 minutes to rake the yard together.