GMAT Quant Chapter 9: Work Problems Flashcards
What are the 4 type of Work problems?
I. Single Worker Problem
II. Combined Workers Problems
III. Opposing Workers Problems
IV. Change in Workers Problems
What are the different versions of the combined work problems?
2 objects work together for the same amount of time
2 objects begin together, 1 stops early
How should we solve a question where one object works for a shorter amount of time than the other?
Time is x for object that stops first
Time is x + y for object that finishes alone
How do we solve a combined work problem where one object has an unknown time?
the rate of the unknown time object is 1/t
(if the job is more than 1 account for this by changing the numerator)
In a combined work problem, how do we compute the contribution of object as fraction or percentage?
time = t (both objects work for the same time)
(rate 1 + rate 2) x time of total work (expressed in terms of t)
Then put the work of the desired object over the total work of both objects to compute the fraction because the ts will cancel out.
What are we allowed to do with objects that work at different rates in combination work problems?
Given a simple example of this.
Add the two seperate rates together.
1/x + 1/y if one object completes a task in x hours and one object completes a task in y hours
How do we solve combined worker problems when object is acting in the opposite direction of another?
Subtract the work done by one object from that done by the other object
What are the 3 forms of the relative work problems?
I. Rate worker 1 as multiple of rate worker 2
II. Rate of one worker slower or faster than rate of another worker
III. Worker 1 completes task in some percent / fraction greater / lesser than the time it takes another worker
How do we solve a work problem where when worker is slower or faster than the other?
object 1: takes x mins + t
object 2: takes t
object 1 rate: 1/(t+x) per min
object 2 rate: 1/t
How can we use x/100 to solve a worker problem where one worker completes a task in some time greater or lesser than another worker doing the same job?
object 1: x percent fewer minutes than object 2
object 2: t
object 1 work time is x (100-x/100) mins
object 1 rate: 1/t(100-x/100) which is equal to 100/t(100-x) job per min
object 2 rate: 1/t job/minute
We can efficiently use the proportion method to solve change in worker problems?
This problem asks the length of time to complete a task when the number of workers is changed (added or subtracted)
x workers / combined rate of x workers (both known from question stem)
=
y workers / combined rate of y workers
