# It takes Bob twice as long as Caitlyn to clean his room. It takes Andrea 10 minutes longer than Caitlyn to clean her room. In total they work 90 minutes to clean their rooms. How long does it take Bob to clean his room?

##### 1 Answer

It takes Bob

#### Explanation:

You will need to use the information provided to you to write three equations with three unknowns.

Let's say that Bob takes

The first piece of information given to you tells you that Bob needs **twice as much** time as Caitlyn to clean his room. This means that you can write

#b = 2 * c#

Next, you were told that Andrea only takes **10 minutes longer** than Caitlyn, which means that you can write

#a = c + 10#

Finally, if you add the time it took all three to clean their rooms, you get

#a + b + c = 90#

Use the value of

#underbrace(c + 10)_(color(blue)(=a)) + overbrace(2c)^(color(red)(=b)) + c = 90#

This is equivalent to

#4c + 10 = 90#

#4c = 80 implies c = 80/4 = color(green)("20 min")#

To find out how long it takes Bob to clean his room, use the first equation

#b = 2c = 2 * (20) = color(green)("40 min")#

Andrea will clean her room in

#a = c + 10 = 20 + 10 = color(green)("30 min")#