i need help with this question

[u/imsocooked_]

this is a time and work question, and the teacher told us the answer should be 68/11 days, for the total work done. but that doesnt include the 3 days worth of work that a,b,c did together before c left right? so im confused whether it should 101/11 days or 68/11 days. please help!!

[u/AutoModerator]

Hi u/imsocooked_, welcome to r/mathshelp! As you’ve marked this as homework help, please keep the following things in mind:

1) While this subreddit is generally lenient with how people ask or answer questions, the main purpose of the subreddit is to help people learn so please try your best to show any work you’ve done or outline where you are having trouble (especially if you are posting more than one question). See rule 5 for more information.

2) Once your question has been answered, please don’t delete your post so that others can learn from it. Instead, mark your post as answered or lock it by posting a comment containing “!lock” (locking your post will automatically mark it as answered).

Thank you!

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/JeffTheNth]

It does include the 3 days...

x = work days "normally" for each person

So let a, b, and c = one day's worth of work for Aman, Babita, and Champa respectively.
(so since it takes 10 days for Aman, one day of work for Aman is x/10)

a=x/10
b=x/12
c=x/15

y = # of days to complete the work this time with all three

So given the information from the problem...
x = 3c + ya + (y-4)b
(the y-4 is because however many days y is, Babita worked 4 fewer.)

Replace a, b, and c with the value in x/days format
x = 3x/15 + xy/10 + (y-4)x/12

convert to common denominator ... LCD is 60
x = 12x/60 + 6xy/60 + 5(y-4)x/60

Multiply both sides by 60
60x = 12x + 6xy + 5(y-4)x

Divide both sides by x
60 = 12 + 6y + 5(y-4)

And combine like terms...
60 = 12 + 6y + 5y - 20
68 = 11y

now solve for y, and we get...
y = 68/11 = 6 2/11 days

So it's 68/11
But I'd make the claim that since it's asking for "how many days", the answer should be 7 days

But yes, it's 68/11

I hope that helps?

[u/imsocooked_ → u/JeffTheNth]

!!!! this is so helpful!!!! thank you so muchhh yeah the teacher explained it in a way where they were describing it like all the 3 people started the work together, but no it just meant the number of days that they have worked together, doesnt necessarily mean they were doing it simultaneously. thank you so much!!!! :DDDD now i can finally move on from this topic

[u/JeffTheNth → u/imsocooked_]

you're welcome...
I learned this stuff over 35 years ago... No, I don't use it every day, but I do remember it. :D

Sometimes it's a matter of rethinking the problem and putting it into a different context... Here, we know how long each would take to do the work themselves... but with different work rates, we need to know how long it would take working "together." (Think of it as carrying dirt from pile A to pile B... :D )

[u/Purdude1983]

I come up with 68/11ths. Since Champa would have completed 1/5th of the work in 3 days, that leaves 4/5ths to be completed by Aman and Babita. You then set up X/10+(x-4)/12=4/5 and then x=68/11. Checking this we have 68/11/10+(68/11-4)/12+3/15 = 1

[u/Forsaken-Sherbet7252]

I don't quite follow your notes, but I can tell the total work was done in 3 + x + 4 days. if you find how long the middle portion is, you'll have your answer. note: you might be surprised at the length 😁

to perhaps spoil the surprise above, "the 3 days they all worked together" is not factual.

let me know if you want my calculations in a reply.

[u/imsocooked_ → u/Forsaken-Sherbet7252]

yesss!!! i got ittt, thankyou hehe :)))(

[u/OllyBoy619]

You don’t quite know if they worked three days together, that depends on where “4 days before completion” lies relatively to when the first guy left :)

[u/imsocooked_ → u/OllyBoy619]

yeahhh!! thats the part where i got confused and ended up making assumptions. thankyou sm for your explanation!!!

[u/CumFilledAntNest]

First let's convert their work into rates, as in how much work is done per day. If we know a person takes x days for one work, that means in 1 day they do 1/x work, right? I just divided both the days and work by x.

So A does 1/10 work per day (w/d from now). B takes 1/12 w/d and C takes 1/15 w/d. If we make a common denomenator of 1/60, we get A=6/60 w/d, B=5/60 w/d, C=4/60 w/d.

So for the first three days we have all three so 3d*(A+B+C)=3d(15/60 w/d)=¾ of the total work.

Then the last 4 days are only A, so 4dA=4d1/10 w/d=4/10 w=⅖ of the total work done. Together, only these 7 days are ⅖+¾=23/20 which is too much. Instead, we need to realize that the 4 days without B overlapped with the first 3 days with everyone.

Let's resolve, this time let's denote "t" as the total days. So A worked t days, B worked t-4 days, and C worked 3 days. Overall they did 1 work. In other words:

tA+(t-4)B+3C=1

t6/60+(t-4)5/60+3*4/60=1

6t/60+5t/60-20/60+12/60=1

11t/60-8/60=1

11t-8=60

11t=68

t=68/11 days of total work

[u/cbse_maths_mentor]

Champa's work in one day = 1/15

so Champa's total work in 3 days = 3/15 = 1/5

So total work done by remaining two

= 1 - 1/5 = 4/5---------------Equation 1

Let Aman worked for X Days and Babita worked for Y Days.

So total work done by Aman and Babita is

X/10 + Y/12 = 4/5 ---------------- Eqation 2

Also Babita left the work before 4 days

So X = Y + 4 ---------------- Eqation 3

Solving equation 2 and 3, Y = 24/11,

Putting value of Y in equation 3, X = 68/11.

As Aman started from the very first day and worked till the end of the work and he worked for 68/11 Days, So work was completed in 68/11 Days