Question

I have no idea how to do this. Pls help. I'll medal.

It takes Arjun 15 hours to install a new deck. Wilbur can install the same deck in 10 hours. If they worked together how long would it take them?

Answer 1

"It takes Arjun 15 hrs to install a new deck." This is a rate, a measurement of how fast this guy Arjun works. You could express this rate as\[\frac{ 1~deck }{ 15~hrs }\]

Answer 2

Do the same for Wilbur.

Wilbur's rate is (you finish):\[\frac{ 1~deck }{ ? }\]

Answer 3

1 deck / 10 hours

Answer 4

Their combined work rate is \[\frac{ 1~deck }{ 15~hrs }+\frac{ 1~deck }{ ? }\]

Answer 5

1 deck/15 hours + 1 deck/10 hours

Answer 6

Good. That's right.

Now divide "1 deck" by this combined work rate. The results will have the units "hrs," whereas "deck" will disappear through cancellation.

Please show all of your work so that I could give you meaningful feedback on what you've done. since the guys hopefully are out to help each other, your answer should be less than both 10 and 15 hours, right?

Answer 7

So would it be 1.5 hours? @mathmale

Answer 8

Either I must ask you to share your work, showing how you got your result, or I must work through the whole problem myself.

Answer 9

Ask yourself: If one guy can do the deck in 15 hours and the other guy in 10, does "1.5 hours" sound appropriate if the two guys are working together??

Answer 10

yeah lol i didn't think it was the right answer

Answer 11

They must be hitting each other over the head to get each to work faster. ;)

Dimensional analysis may help you to solve this problem properly.

What would the units of measurement be if you were to simplify the following?


1 job
------------------------- = ?
1 job 1 job
------- + --------
15 hr 10 hr

Answer 12

Hint: Combine (1 job / 15 hr) and (1 job / 10 hr).

Answer 13

1 job
--------------------------
2 jobs
-------
25 hours

?

Answer 14

Identify and use the LCD.

Answer 15

LCD is 5

Answer 16

will 10 divide into 5 with an integer result?
will 15 divide into 5 with an integer result?

Think about how you would combine:\[\frac{ 1 }{ 10 }~ and~\frac{ 1 }{ 15 }\]

Answer 17

ohh you multipled the numerator by how many times the denominator equals with the other denominator so it'll be

3/30 + 2/30 = 5/30 = 1/6

@mathmale

Answer 18

Think about how you would combine
\[\frac{ 1 }{ 10 }~and~\frac{ 1 }{ 15 }\]

Answer 19

Your result is correct. The LCD is 30. Very good. so, in your denominator you have the combined work rate \[\frac{ 1~job }{ 6~hours }\]

Answer 20

How are you going to use this to find the number of hours the 2 guys require to do the entire job, working together?

Answer 21

the 6 is the amount of hours it takes for both of them

Answer 22

@mathmale

Answer 23

Yes. Simplify that: "Working together, the two boys could complete this job in 6 hours."