A man paints a house in 3 hrs, another man paints the same house in 5hrs. How long would it take together plz

Question

What i am looking for is the RULE to work out this answer quick and easly with different inputs.
Yes both men take the same time every time they paint the house , and no they do not have breaks or get board and leave the job. ( like some of the answers i have had)
thanks all for trying jug

Answer 1

1/3x + 1/5x = 1

15(1/3x) + 15(1/5x) = 15(1)

5x + 3x = 15

8x = 15

8x / 8 = 15 / 8

x = 15/8

x = 1 7/8 hours

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Find the minutes.

7/8 of 60 =

7/8(60) =

420/8 =

52.5 minutes

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The two men together can paint the house in 1 hour 52 minutes.

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Answer 2

If the first guy can paint a house in 3 hours, he can paint (1/3) of a house in 1 hour. Similarly the second guy can paint (1/5) of a house in 1 hour. So working together they can paint (1/3+1/5 = 5/15+3/15 = 8/15) of the house in 1 hour, so it should take 15/8 hours to complete the job together.

As a rule, if it takes one person x hours and the second y hours, together it should take them 1/[1/x+1/y] hours. You can extend it for more people too (add a third person who takes z hours, and it would become 1/[1/x+1/y+1/z]).

Answer 3

The rule is that the times don't add up... the speeds do.

Speed of man 1 = 1/3 house per hour.
Speed of man 2 = 1/5 house per hour.

Speed Together = 1/3 + 1/5 = 8/15 house per hour.
So they will take 15/8 hours to do the job.

Answer 4

In 1 Hour 1/3 of a house gets painted and 1/5 house gets painted.

Total amount of house = 1/3 + 1/5 = 8/15th

So 15/8 hours is needed!

General rule T = 1/Sigma i=1,n (1/Ri)

Answer 5

in 1 hour,the first man paints 1/3rd of the house whereas in 1 hour ,the second man paints 1/5 th part of the house
Therefore working together in 1 hour they paint (1/3+1/5 or)8/15 part of the house
Hence they would take 1 divided by 8/15 or 15/8 or 1 7/8 hours to paint the house

Answer 6

I always use this equation:

time together / time alone1 + time together / time alone2 = 1

Let's call T the time it takes them do paint the house together:

T/3 + T/5 = 1

5T + 3T = 15
T = 15/8

Yoy may notice this is (5*3) / (5+3). That little trick works for very basic problems like this when the two workers are working for the same amount of time together.

Answer 7

Why don't you go for a practical demonstration ? Then deduce a Rule from that and share it with the world !

Answer 8

(time together / time alone) + (time together / time alone) = 1

So in your case...
x / 3 + x / 5 = 1

Multiply everything by 15 to get rid of the fractions...
5x + 3x = 15
8x = 15
x = 1.875

Answer 9

call me... is so smart and should be a teacher. no one has ever broken it down like that. If I were to have had a teacher who put it like that , i would have never had any trouble.

kudos to you!