trey can clean a room in 40 minutes. his brother Marcus can clean the same room in 20 minutes. how long will it take them to clean the room if they work together?
Trey's rate = 1/40
Marcus rate = 1/20
combined rate = 1/40 + 1/20 = 3/40
time at combined rate = 1/(3/40)
= 40/3 minutes
To calculate how long it will take Trey and Marcus to clean the room together, we can find their combined cleaning rate.
Trey's cleaning rate is 1 room per 40 minutes, which can be written as 1/40 rooms per minute.
Marcus's cleaning rate is 1 room per 20 minutes, which can be written as 1/20 rooms per minute.
To find their combined cleaning rate, we can add their individual rates together:
1/40 + 1/20 = 3/40
So, together, Trey and Marcus can clean 3/40 of a room per minute.
To find how long it will take them to clean the whole room together, we can calculate the reciprocal of their combined cleaning rate:
1 / (3/40)
We can simplify this expression by multiplying the numerator and denominator by the reciprocal of the fraction inside the parentheses:
1 / (3/40) = 1 * (40/3) = 40/3
Therefore, it will take Trey and Marcus approximately 40/3 minutes to clean the room together, which is approximately 13.33 minutes.
To find out how long it will take Trey and Marcus to clean the room when they work together, we can use the concept of work rate.
First, we need to determine their individual work rates. Trey can clean the room in 40 minutes, so his work rate would be 1 room per 40 minutes, or 1/40 rooms per minute. Similarly, Marcus can clean the room in 20 minutes, so his work rate would be 1 room per 20 minutes, or 1/20 rooms per minute.
To find their combined work rate when working together, we can simply add their individual work rates. So, Trey and Marcus' combined work rate would be (1/40 + 1/20) rooms per minute, which equals 3/40 rooms per minute.
Now, we can use the combined work rate to find how long it will take them to clean the room together. We can set up a proportion:
(3/40) rooms per minute = 1 room / x minutes
To solve for x, we can cross-multiply:
3x = 40
Divide both sides by 3 to isolate x:
x = 40 / 3
Therefore, it will take Trey and Marcus approximately 13.33 minutes to clean the room if they work together.