# Math Help - GMAT Combined Work Problems

1. ## GMAT Combined Work Problems

Every time I come across a GMAT combined work problem it throws me off. I found a strategy that I thought would work for me, but I came across a few problems in which I did not know how to apply the strategy. Can someone please help me out?

The strategy uses a table in which the formula Velocity = Distance/Time is used.

Since the independent people or things are doing the same activity, the distance remains a constant, which is 1.

In a simple problem, this is how the strategy would be applied:

If Sam can finish a job in 3 hrs and Mark in 12 hrs, in how many hrs can they finish the job if they worked on it together at their respective rates?

Solution:

V D T
S 1/3 1 3

M 1/12 1 12

S+M V(s+m) 1 X

___________________________________
S 1/3 1 3

M 1/12 1 12

S+M 5/12 1 T

So, to solve for V(s+m) 1/3 +1/12 = V(s+m)
5/12 = V(s+m)

Now, to solve for the time V= D/T

5 = 1
12 T Solving for T, T = 2 2/5 hrs

So, using this methodology, how would I solve the following problems?
I would like to use a consistent approach for solving these types of problems so that I am not confused at the time of taking the GMAT. Thanks for your help.

Working together, Bill & Tom painted a fence in 8 hrs. Last year Tom painted the fence by himself. The year before, Bill painted the fence by himself, but it took 12 hrs less than Tom took. How long did Bill and Tom take when each was painting alone?

Last Thursday John assembled chairs at a rate of 3 chairs per hour for part of the day and Larry assembled no chairs. Last Friday, Larry assembled chairs at a rate of 4 chairs per hour for part of the day and John assembled no chairs. If during these two days, John and Larry assembled a total of 25 chairs over 7 hours, how many chairs did John assemble last Thursday?

2. Originally Posted by DKRbella0814
If Sam can finish a job in 3 hrs and Mark in 12 hrs, in how many hrs can they finish the job if they worked on it together at their respective rates?
Set up a ratio $\displaystyle \textrm{Hours}:\textrm{Proportion of Job Completed}$ for each Sam and Mark...

Sam

$\displaystyle 3 : 1$

$\displaystyle 1 : \frac{1}{3}$.

Mark

$\displaystyle 12 : 1$

$\displaystyle 1:\frac{1}{12}$.

So if they were to do the job together, every hour they would complete $\displaystyle \frac{1}{3} + \frac{1}{12} = \frac{4}{12} + \frac{1}{12} = \frac{5}{12}$ of the job.

So together, the ratio is

$\displaystyle 1 : \frac{5}{12}$

$\displaystyle 12:5$

$\displaystyle \frac{12}{5}:1$.

So together they will complete the job in $\displaystyle \frac{12}{5} = 2.4$ hours.

3. I can solve the first one.
Let Bill's work be $x$ and Tom's work be $y$.
then,as per given data you get 2 equations.
$\frac{1}{x}+\frac{1}{y}=\frac{1}{8}$.......1
and, $y=x-12$..........2
substituting, you get a quadratic equation. Solve it. Of 2 answers, 1 is not possible.

4. In "combining work problems", it is the rate of work that adds.

Working together, Bill & Tom painted a fence in 8 hrs. Last year Tom painted the fence by himself. The year before, Bill painted the fence by himself, but it took 12 hrs less than Tom took. How long did Bill and Tom take when each was painting alone?
Let T be the time, in hours, Tom took to finish the job. Tom's rate is $\frac{1}{T}$ "job per hour". Bill took 12 hours less than Tom to his time was $T- 12$ hours and his rate was $\frac{1}{T- 12}$ "job per hour".

Working together their combined rate is $\frac{1}{T}+ \frac{1}{12}= \frac{12+ T}{12T}$ "job per hour" and that is equal to $\frac{1}{8}$ because they took 8 hours together. Solve $\frac{12+ T}{12T}= \frac{1}{8}$ to determine how long Tom took, then subtract 12 hours to determine how long Bill took.

Last Thursday John assembled chairs at a rate of 3 chairs per hour for part of the day and Larry assembled no chairs. Last Friday, Larry assembled chairs at a rate of 4 chairs per hour for part of the day and John assembled no chairs. If during these two days, John and Larry assembled a total of 25 chairs over 7 hours, how many chairs did John assemble last Thursday?
Let J be the number of hours John worked assembling chairs. The total number of chairs he assembled was 3J. Let L be the number of hours Larry assembled chairs. The total number of chairs he assemble was 4L.

Since they worked a total of 7 hours, J+ L= 7. Since they assembled 25 chairs, 3J+ 4L= 25. Solve those two equations, perhaps by replacing "L" in the second equation by L= 7- J from the first equation.