Question

If it took Matt 6 hours to clean alone, and two cleaners can clean in 2 hours, how long will it take Mark to clean alone?

Answer 1

If it takes Matt 6 hours to clean alone and two cleaners can clean in 2 hours, it will take Mark 2/3 hours to clean alone.

Step-by-step explanation:

Let's assume that Mark takes x hours to clean the room alone.

First, let's calculate the rates at which Matt and the two cleaners work.

Since Matt takes 6 hours to clean alone, his cleaning rate is (1 room)/(6 hours) = 1/6 rooms per hour.

Since two cleaners can clean in 2 hours, their cleaning rate is (1 room)/(2 hours) = 1/2 rooms per hour.

Now, let's set up an equation based on the time it takes for each person to clean the room:

Matt's cleaning rate + Two cleaners' cleaning rate = Mark's cleaning rate

1/6 + 1/2 = 1/x

Now, we solve for x:

1/x = 1/6 + 1/2

1/x = (1 + 3)/6

1/x = 4/6

1/x = 2/3

Therefore, Mark's cleaning rate is 1/(2/3) = 3/2 rooms per hour.

So, it will take Mark (1 room)/(3/2 rooms per hour) = 2/3 hours to clean the room alone.