SOLUTION: I am doing a review for my nursing students at the college where I teach. I am having trouble showing them the steps to solve a problem like below. Tim paints a room in 2.5 hour

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Question 634178: I am doing a review for my nursing students at the college where I teach. I am having trouble showing them the steps to solve a problem like below.
Tim paints a room in 2.5 hours. Bob paints a room the same size in 5 hours. How long would it take them if they painted the room together?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1/2.5 + 1/5 = 1/t

10/25 + 1/5 = 1/t

10t + 5t = 25 ... Multiply every term by the LCD 25t to clear out the fractions

15t = 25

t = 25/15

t = 5/3

t = 1%262%2F3

So if they worked together, then it would take them 1%262%2F3 hours (or 1 hour, 40 minutes)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Tim paints a room in 2.5 hours. Bob paints a room the same size in 5 hours. How long would it take them if they painted the room together?
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Tim time: 2.5 hrs/job ; rate = 1/2.5 job/hr
------
Bob time: 5 hrs/job ; rate = 1/5 job/hr
----
Together time: x hrs/job ; rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/2.5 + 1/5 = 1/x
----
1/(5/2) + 1/5 = 1/x
---
(2/5) + 1/5 = 1/x
----
3/5 = 1/x
x = 5/3 = 1 2/3 = 1 hr 40 minutes (time to do the job together)
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Comment: Post your problem again and you will probably see a different
method for this type of problem.
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Cheers,
Stan H.