159k views
1 vote
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?

1 Answer

2 votes

Final answer:

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.

User Shennan
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories