Word Problem Troubles

[smitty0405]

I'm studying for the TEAS test. I have come across this problem and have no idea how to solve it. This is just an example.

John can paint a room in 2 hours. Sue can do it in 6 hours, and Tim can do it in 4 hours. How long does it take them to do it together?

I'm not looking for the answer, but HOW to solve it.


My other problem is with a question like this

There are 4 blue socks, 8 red, and 4 yellow. How many have to be taken out to ensure a pair?

Thank you.

 

[Deleted member 4993]

I'm studying for the TEAS test. I have come across this problem and have no idea how to solve it. This is just an example.

John can paint a room in 2 hours. Sue can do it in 6 hours, and Tim can do it in 4 hours. How long does it take them to do it together?

I'm not looking for the answer, but HOW to solve it.


My other problem is with a question like this

There are 4 blue socks, 8 red, and 4 yellow. How many have to be taken out to ensure a pair?

Thank you.

For the second problem:

if you pick three socks - you can have one each color - and no pair for sure.

Now what happens....

 

[soroban]

Hello, smitty0405!

John can paint a room in 2 hours. Sue can do it in 6 hours, and Tim can do it in 4 hours.
How long does it take them to do it together?

Here's my baby-talk approach to these "work" problems.


\(\displaystyle \text{John does the job in 2 hours.}\)
. . \(\displaystyle \text{In one hour, he can do }\tfrac{1}{2}\text{ of the job.}\)
. . . . \(\displaystyle \text{In }x\text{ hours, he can do }\tfrac{x}{2}\text{ of the job.}\)

\(\displaystyle \text{Sue does the job in 6 hours.}\)
. . \(\displaystyle \text{In one hour, she can do }\tfrac{1}{6}\text{ of the job.}\)
. . . . \(\displaystyle \text{In }x\text{ hours, she can do }\tfrac{x}{6}\text{ of the job.}\)

\(\displaystyle \text{Tim does the job in 4 hours.}\)
. . \(\displaystyle \text{In one hour, he can do }\tfrac{1}{4}\text{ of the job.}\)
. . . . \(\displaystyle \text{In }x\text{ hours, he can do }\tfrac{x}{4}\text{ of the job.}\)


\(\displaystyle \text{Working together for }x\text{ hours, they complete the job (1 job).}\)

\(\displaystyle \text{There is the equation: }\quad \frac{x}{2} + \frac{x}{6} + \frac{x}{4} \;=\;1\)


\(\displaystyle \text{Got it?}\)