SOLUTION: Noni can paint his garage in 3 1⁄2 hours while his friend Anton can paint it in 4 hours. If they work together, if they started at 4:00 P.M. at what time they will finish the sai

Algebra ->  Systems-of-equations -> SOLUTION: Noni can paint his garage in 3 1⁄2 hours while his friend Anton can paint it in 4 hours. If they work together, if they started at 4:00 P.M. at what time they will finish the sai      Log On


   

Question 1194895: Noni can paint his garage in 3 1⁄2 hours while his friend Anton can paint it in 4 hours. If they work together, if they started at 4:00 P.M. at what time they will finish the said job?
Found 4 solutions by josgarithmetic, ikleyn, math_tutor2020, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F3%261%2F2%2B1%2F4

1%2F%287%2F2%29%2B1%2F4

2%2F7%2B1%2F4

8%2F28%2B7%2F28

15%2F28------------rate for 1 job, "paint the garage";


28%2F15 HOURS per GARAGE, the two of the friends working together; this is , in hours, 1%2613%2F15 or 1 hour 52 minutes.

Answer by ikleyn(52890) About Me  (Show Source):
You can put this solution on YOUR website!
.
Noni can paint his garage in 3 1⁄2 hours while his friend Anton can paint it in 4 hours.
If they work together, if they started at 4:00 P.M. at what time they will finish the said job?
~~~~~~~~~~~~~~~~~~ 

Noni can do the job in 3 1/2 hours, or in 210 minutes.

So, Noni's rate of work is 1/210 of the job per minute.



Anton can do the job in 4 hours, or in 240 minutes.

So, Anton's rate of work is 1/240 of the job per minute.



Their combined rate of work is the sum of individual rates 

   1%2F210+%2B+1%2F240 = %281%2F30%29%2A%281%2F7+%2B+1%2F8%29 = %281%2F30%29%2A%288%2F56%2B7%2F56%29 = %281%2F30%29%2A%2815%2F56%29 = 1%2F112

of the job per minute.



Hence, working together, they will complete the job in 112 minutes = 1 hour and 52 minutes.


So, they will complete the job at 5:52 pm.    ANSWER

Solved.

------------------

It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Multiply the two time values together:
3.5*4 = 14

Then let's say we stick a 0 at the end to get 140. Just so there's more wall area to work with.

Let's say the garage walls are 140 square feet.

Noni needs 3.5 hours to get the job done on his own. His unit rate is 140/(3.5) = 40 square feet per minute.

Anton needs 4 hours to get the job done on his own. His unit rate is 140/4 = 35 square feet per minute.

As you can see, I chose the number 140 so that the results of the division operations above were nice whole numbers.
Once again, you could have used 14 instead of 140, but 140 seems more realistic for a total wall area to paint.
I'll leave it to the student to decide which she or he prefers better.

Add the two unit rates: 40+35 = 75
If the two men work together, and do not get in each other's way, then their combined unit rate is 75 square feet per minute.
This only applies to the 140 total square feet needed to be painted.

x = number of hours needed if the two men work together (without slowing each other down)


(rate)*(time) = amount done
(75 sq ft per hr)*(x hrs) = 140 sq ft
75x = 140
x = 140/75
x = (28*5)/(15*5)
x = 28/15

They will take exactly 28/15 hours if they work together most efficiently.
This improper fraction isn't exactly clear how long it will take.

Let's convert it to something more familiar time duration.
28/15 = (15+13)/15
28/15 = 15/15+13/15
28/15 = 1+13/15
28/15 = 1 & 13/15
They will take one hour, plus 13/15 of another additional hour (i.e. nearly 2 hours)

Convert the 13/15 of an hour to minutes only
13/15 hr = (13/15)*60 = 52 min

Therefore,
28/15 hr = 1 hr & 52 min
we can think of it as
28/15 hr = 1 & 52/60 hr = 1 hr + 52/60 hr
if you wanted.

Anyways, the total duration is 1 hr & 52 minutes if they work together.

Add this duration to 4:00 PM and we arrive at 5:52 PM as the final answer

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
Noni can paint his garage in 3 1⁄2 hours while his friend Anton can paint it in 4 hours. If they work together, if they started at 4:00 P.M. at what time they will finish the said job?
Let time they take, working together, be T

Then Noni's and Anton's per-hour rates are: matrix%281%2C3%2C+1%2F3.5%2C+and%2C+1%2F4%29, respectively

We then get: matrix%281%2C3%2C+1%2F3.5+%2B+1%2F4%2C+%22=%22%2C+1%2FT%29

           4T + 3.5T = 14 ------ Multiplying by LCD, 4T(3.5)

                7.5T = 14

Working together, time both will take to complete job, or 

Time when both will finish job: