Nidhi's project

Together, Alice and Bob work $\frac{1}{20}+\frac{1}{30}=\frac{5}{60}=\frac{1}{12}$ , so it takes them $12$ days to finish the project when they work together. For the last $10$ days, it is just Bob working, and he finishes the project in $30$ days alone; thus, he completes $\frac{10}{30}=\frac{1}{3}$ of the project in this time. So, when Alice and Bob work together, they complete $\frac{2}{3}$ of the project, which takes $12\frac{2}{3}=8$ days, so the total is $8+10=\boxed{18}$

As the question stated, Alice can complete the project in 20 days, Bob can complete the project in 30 days.

So this means that Alice can complete $\frac{1}{20}$ of project in a day, and Bob can complete $\frac{1}{30}$ of project in a day.

If Alice and Bob works together, them are able to done $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{1}{12}$ of project in a day.

Alice quits 10 days before the project is complete, means that Bob will be doing the last part which is $\frac{1}{30}$ * 10 = $\frac{1}{3}$ of the project.

Alice will help at the rest (1 - $\frac{1}{3}$ = $\frac{2}{3})$ of the project, them used $\frac{2}{3}$ / $\frac{1}{12}$ = 8 days to done the $\frac{2}{3}$ of the project.

In total, them used 8 + 10 = 18 days to complete the whole project.

Alice and Bob work at a constant rate of 1/20x and 1/30x respectively. (Alice completes 1/20th of the job and Bob completes 1/30th of the job per day. x is the total number of days it will take to complete the project) Knowing that Alice quits 10 days before the project is complete, we subtract 10 from x, giving the following equation:

1/20(x-10)+1/30x=1

Solving for x gives us 18 days.

Alice é capaz de fazer $\frac{1}{20}$ do projeto por dia. Já Bob faz $\frac{1}{30}$ . Seja $n$ o total de dias trabalhados pelos dois juntos para completar todo o projeto. Se Alice não trabalha os 10 últimos dias, isso será descontado. Temos então que $n \times (\frac{x}{20} + \frac{x}{30}) - 10 \times \frac{x}{20} = x$ . Resolvendo para $n$ chegamos em $n = 18$ dias.

A have a speed $\frac{1}{20}$ and B have a speed $\frac{1}{30}$ and A+B have a speed $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{1}{12}$ . B is working alone for 10 days it means $\frac{10}{30}$ project have complete, and the rest their working together but only working 1- $\frac{1}{3}$ project or $\frac{8}{12}$ project. because their speed is $\frac{1}{12}$ their finish $\frac{8}{12}$ project in 8 days. so the total days is 10 + 8 = 18 days

The rate each person completes the project is the inverse of the days it takes to complete $rate A = \frac {1} {20}, rate B = \frac {1} {30}$ B stays 10 more days than B $B = A + 10$ Formulate the equation where A is the number of days A works and B is the number of days B works

It will add to one as we only want one project to be completed $\frac {1} {20} A + \frac {1} {30} B = 1$ $\frac {1} {20} A + \frac {1} {30} (A + 10) = 1$ $\frac {3} {2} A + A + 10 = 30$ $\frac {3} {2} A + A = 20$ $3A + 2A = 40$ $5A = 40$ $A = 8$ Total project length is B so $B = 8 + 10$ $B = 18$

Alice alone can complete $\frac{1}{20}$ of project per day.

Bob alone can complete $\frac{1}{30}$ of project per day.

So, if they work together, they can complete:

$\frac{1}{20} + \frac{1}{30} = \frac{1}{12}$ of project per day.

Alice quits 10 days before the project is complete.

In 10 days, Bob can done $\frac{1}{30} \times 10 = \frac{1}{3}$ of project.

So actually, Alice and Bob work together only for $\frac{2}{3}$ of the project.

If $Y$ is the time that Alice and Bob need to complete $\frac{2}{3}$ of the project, then:

$\frac{2}{3} = \frac{1}{12} \times Y$

$12 \times \frac{2}{3} = Y$

$8 = Y$

So, the project complete in:

10 ( Bob works alone ) + 8 ( Alice and Bob work together ) = 18 days

1/20+1/30=1/12. it will take 12 days if both of them work together on the project. since alice quits 10 days before the completion, only bob worked for the last 10 days. 10/30=1/3 of the project is done in the last 10 days. Which means 2/3 of the project is done at a rate of 1project/12days => (2/3)/(1/12)= 2/3 * 12 = 8days. 8+10= 18days

alice's rate is 1/20 and bob's rate is 1/30

their rate combine is 1/20+1/30=1/12

Suppose Alice quits after x days,

then during those x days, together, at the rate of 1/12. They finished x/12 of the project.

it takes Bob another 10 days to complete the project.what is the total days to complete the project

Then during those 10 days, together, at the rate of 1/30.Bob finished 10/30

x/12+1/3=1

x=8

Alice and Bob work for 8 days and Bob works alone for 10 days

8+10=18

Alice do per day = 1/20 Bob do per day = 1/30

Both can do per day = 1/20 + 1/ 30 = 1/12

So, both can complete whole work in = 12 days

Only Bob do work in 10 days = 10/30 = 1/3 so, remaining 2/3 is done by both in 12 * 2/3 = 8 days. so, total work needs = 10 + 8 = 18 days.

Since Alice can complete a project in 20 days and bob can complete it in 30 days, we can deduce that Alice completes 1/20th of a project per day and Bob completes 1/30th of a project per day.

A = 1/20

B = 1/30

We can multiply either of these rates by x number of days to determine how many projects will be completed in that time frame.

(Rate)(x days) = Amount of projects completed

Since we know Bob and Alice start work on a project on the same day, and Alice quits 10 days before the project is complete, our formula looks like this:

(1/20) * (x - 10) days + (1/30) * x days = 1 project

Now we can solve for x:

1/20 * x - 10/20 + 1/30 * x = 1

(1/20 + 1/30) * x - 1/2 = 1

(3/60 + 2/60) * x = 1 + 1/2

5/60 * x = 3/2

1/12 * x = 3/2

x = 3/2 * 12

x = 18

It takes Alice and Bob 18 days to complete the project.

Working alone, Alice will complete $\frac{1}{20}$ of the project in one day. Bob can complete $\frac{1}{30}$ of the project per day. If x is the number of days that Alice works, then $\frac{x}{20}$ is the fraction of the project Alice completes and $\frac{x}{30}$ is the fraction that Bob completes. Bob works an additional ten days to do the final $\frac{10}{30}$ of the project, so our equation is $\frac{x}{20}$ + $\frac{x}{30}$ + $\frac{10}{30}$ = 1. Solving for x gives 8, the number of days that Alice works. Bob works 10 days longer than Alice, so the total number of days is 18.

Firstly, lets consider the rate at which Alice and Bob complete the project.

Alice takes 20 days to complete one project, so Alice does $\frac{1}{20}$ of a project per day.

Bob takes 30 days to complete one project, so Bob does $\frac{1}{30}$ of a project per day.

The problem can be split into two sections:

• An unknown length of time when both are working on the project, and
• A known length of time (10 days) when only Bob is working on the project.

For simplicity's sake, lets consider the known length of time first.

Bob takes 10 days to finish the project. At his rate, Bob can do $\frac{1}{30} \times 10 = \frac{1}{3}$ of the project. This means that at the beginning of the 10 day period, the project was $\frac{2}{3}$ complete.

Now lets consider the first section, by intitially calculating their combined rate of completion.

Combined Rate $=$ Alice's rate $+$ Bob's rate $=\frac{1}{20}+\frac{1}{30}=\frac{5}{60}=\frac{1}{12}$ .

This means that they need 8 days to complete the first $\frac{2}{3}$ of the project ( $\frac{1}{12} \times 8 = \frac{2}{3}$ ).

This means that the total completion time for the project is $8+10=18$ days.

let x be the whole complete project done.

Alice does x/20 amount of work everyday

Bob does x/30 amount of work everyday

for the number of days they work together, k, the amount of work done is:

k (x/20) + k (x/30) = k (x/20+x/30) = k (x/12)

in the last 10 days, only Bob does work. the amount of work done by him in the last 10 days is:

10(x/30) = x/3

Adding up all the work completes the project. hence:

k(x/12) + x/3 = x

k/12 + 1/3 = 1

k/12 = 2/3

k = 8

the number of days they work together is 8, but adding the days worked together, and the days Alice didn't work, gives the total days:

hence total days = 8 + 10 = 18

really simple, in 10 days Bob can do 1/3 of the project so we have to discover how much time they need togheter to do 2/3. in 25 days they do 2 projects togheter, to do 2/3 they need 8.3, so 18 days

Alice, 1/20 por dia Bob, 1/30 por dia

Nos últimos 10 dias, apenas Bob trabalha, portanto 1/3 do tempo

Em 2/3 do tempo, ambos trabalham

1/20+1/30 = 5/60

5/60 por dia

2/3 = 40/60

Portanto, gastarão 8 dias

18 dias

Alice : 1/20 project per day. Bob : 1/30 project per day. Alice and bob working together, 1/20 + 1/30 = 5/60. so if they working together a project will finished in 12 days. 10 days bob to complete project it means 1/3 project. 2/3*12 + 10 = 18 days.

assume the project to be unity. that is 1. then calculate the rates of doing work for each member. that is (1/20) for alice and (1/30) for bob. now for x number of days they work together. so (1/20 +1/30)x part of project is completed. the remaining part of project is completed by bob that is (1/30)10. Now equqtion of project becomes (1/20 +1/30)x +(1/30)10 = 1. solve this to get x. and the required answer will be x+10 that is 18.

Create variable t for number of days taken in total.

Set up the equation:

t(1/30) + (t-10)(1/20) = 1

which is, Bob's rate times all the days (all the work he did) plus Alice's rate times all the days sans 10 (all the work she did) equals 1 (the finished project).

Solve, and get 18 for t.

If it takes Bob 10 days to finish the project after Alice left we know that the project was 2/3 of the way done before she left (10/30 = 1/3 done by Bob after Alice left). From there you just have to find the number of days it took Alice and Bob to get 2/3 done. Based on their rate of work 8/20 + 8/30 = 2/3 so they were working together for 8 days. 8+10=18 total days needed for the project to be finished

In one day, Alice completes $\frac{1}{20}$ of the project, and Bob completes $\frac{1}{30}$ . When they work together, we add up their respective rates and see that they complete $\frac{1}{12}$ of the project every day.

Let's say Alice quits after day $t$ . So after working together for $t$ days and Bob working alone for $10$ days, they complete the project. Thus $\frac{1}{12}t+(\frac{1}{30})10 =1$ . Solving this equation we see, $t=8$ , and therefore the project took $18$ days to complete.

Since Alice can complete a work in 20 days, then in 1 day she can complete 1/20 of the work, while in x days, x/20. Bob can finish x/30 in 1 day. So the working equation is

$\frac{1}{20}$ + $\frac{1}{30}$ (x+10) = 1

Because Alice worked for x days, and Bob worked 10 days alone AFTER Alice had helped him, so x+10.

In one day, Alice finishes 1/20 of the job. In one day, bob finishes 1/30 of the job. Let the job be 1, and since Bob does 10 days by himself, he does 1/3 of the job, leaving us with 2/3 of the job. When Alice and Bob work together, they finish (1/20)+(1/30)=(1/12) in one day. Now let x be the number of days they work together, then (1/12)x=(2/3), so x=8, so the total number of days is 10+8=18

Lets the total number of days to complete Nidhi's project is x.

For Alice it will take 10 days less (1/20)(x - 10).

For Bob it will take (1/30)(x).

Now after adding both of their work, the work will get completed then the equation which we get is.

(1/20)(x - 10) + (1/30)(x) = 1

Therefore x = 18 days.

So, it takes 18 days to complete Nidhi's Project..

Let the total work is 1

Bob and Alice can do the work together $1/20+1/30 = 5/60 or 1/12$

And they will finish there work in 12 days.

Let the total days of the work is x .

Then, they together worked $x - 10$ days

And Bob separately worked 10 day.

Bob done the work in last 10 days = $10*1/30 = 1/3$

Remaining work = $1 - 1/3 = 2/3$

And we get the equation :

$1/12(x-10 = 2/3$

Solving the equation we get the answer and the value of x = $18$

First of all, let us note that for $1$ -day's work, Alice completes $\frac{1}{20}$ of the project, Bob completes $\frac{1}{30}$ of it, whereas they both complete $\frac{1}{12}$ of the project ( $\frac{1}{20}+\frac{1}{30}$ ).

Let us assume that $x$ is the number of days required to complete the project with all the circumstances taken into account. That lets us know that the time Bob and Alice actually work together is $x-10$ , since Alice quits exactly $10$ days before the end of the project. Consequently, Bob works alone the last $10$ days. Therefore, we have a linear equation

$\frac{1}{12}\cdot(x-10)+10\cdot\frac{1}{30}=1\Rightarrow x=18$ .

Thus, the total number of days it will take to complete the project is $18$ .

Let x represent the number of total days they have spent on the project.

We will be using this statement. 1/20 is the amount of work Alice does per day, while 1/30 is the amount of work Bob does per day. If you put them in a statement, we are trying to find x when everything equals to 1, which is one complete project.

(x-10)(1/20) + (x)(1/30) = 1

Next, solve for x. Expand everything.

1/30x + 1/20x - 1/2 = 1

1/12x = 3/2

x = 18

Let the project consist of 60 units: Alice works at a rate of 3 units/day to complete it in 20 days. Bob works at a rate of 2 units/day to complete it in 30 days.

Let x = total number of days to complete the project.

We can write the equation: 3A + 2B = 60 where 3 is the rate at which Alice Works, 2 is the rate at which Bob works. A is the number of days that Alice works, and B is the number of days that Bob works.

A = X - 10 B = X

If we substitute we get the equation: 3(X-10) + 2X = 60

Solve for X to get 18.

Everyday, Alice can finish $\frac{1}{20}$ of the project

Everyday, Bob can finish $\frac{1}{30}$ of the project

Everyday, Alice and Bob can finish $\frac{1}{12}$ of the project together

Since Bob did the final 10 days of the project by himself, it means that he did the final $\frac{1}{3}$ of the project by himself, in 10 days.

Therefore, before Alice left, they had done together $\frac{2}{3}$ of the project.

The time it took for them to finish that earlier $\frac{2}{3}$ of the project =

$\frac{2}{3}$ / $\frac{1}{12}$ = 8 days

Therefore, it took them 8+10 = 18 days to finish the project.