GMAT Avengers Study Group: Work Rate Problems:

by on February 9th, 2015

When the rate is a rate of work being done, then when two people work together, their combined rate is the SUM of their respective individual rates. We need to make sure what are we adding are the rates, not anything else.

A rate is how fast something is growing, changing, or being performed. The overarching rate formula is:

Amount = Rate * Time

When the rate is a speed, this simplifies to the familiar formula:

Distance = Speed * Time

What is a ‘Work’ Word Problem?

  • It involves a number of people or machines working together to complete a task.
  • We are usually given individual rates of completion.
  • We are asked to find out how long it would take if they work together.

For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job.

Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job.

Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.

Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

The vast majority of work problems on the GMAT involve two people or two machines and comparisons of their individual production to their combined production.(rate of A alone) + (rate of B alone) = (combined rate of A & B)

Here A and B can be two people, two machines, etc. For example, if we have N identical machines, and each works at a rate of R, then the combined rate is N*R.

Understand that it is important to know and realize that rates are just ratios. This means we can solve these problems by setting up proportions and using proportional thinking. This is a very powerful strategy to know.

The links to the articles shared on the Facebook Event Page are as follows:

Practice Problems

Problem Solving

1) When Mary paints a house, it takes her 4 hours. When Lisa joins Mary, and they work together, it takes them only 3 hours to paint a house of the same size. How long would it take for Lisa to paint a house of the same size by herself?

(A) 5 hr

(B) 6 hr

(C) 7 hr

(D) 12 hr

(E) 20 hr

2) Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 15

3) Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

(A) 4

(B) 6

(C) 8

(D) 10

(E) 12

4) Two musicians, Maria, and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?

(A) 1 hr 20 min

(B) 1 hr 45 min

(C) 2 hr

(D) 2 hr 20 min

(E) 3 hr

5) Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 4,800 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 800 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip?

(A) 12:00

(B) 13:00

(C) 13:30

(D) 14:00

(E) 16:00

6) A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

(A) 5 (5/11) minutes

(B) 6 minutes

(C) 10 minutes

(D) 19 minutes

(E) 30 minutes

Data Sufficiency (Sample answer choices are given below)

  • Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • EACH statement ALONE is sufficient to answer the question asked.
  • Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

1) Two chefs, Chef Andrew and Chef Bonnie, were hired to prepare a dinner. The two chefs began working at the same time, but Chef Andrew was only able to work for 2 hours. How many hours did it take Chef Bonnie, working alone, to finish making the dinner?

(A) Working alone, Chef Andrew made 1/4 of the meal.

(B) It would have taken 6 hours for Chef Bonnie to cook the entire meal herself.

2) Jane can paint the wall in J hours, and Bill can paint the same wall in B hours. They begin at noon together. If J and B are both even numbers is J=B?

(A) Jane and Bill finish at 4:48 p.m.

(B) (J+B)^2=400

3) A newer machine, working alone at its constant rate, can fill a production order in half the time required by two older machines working together at their constant rates. If the three machines are used together, will they require more than 1 hour to fill a production order?

(A) Each of the older machines, working alone at its constant rate, can fill half a production order in less than 4 hours.

(B) If the newer machine were to double its rate, it could fill a production order working alone in less than one hour.

4) If machine J, working alone at its constant rate, takes 2 minutes to wrap 60 pieces of candy, how many minutes does it take machine K, working alone at its constant rate, to wrap 120 pieces of candy?

(1) Machine K, working alone at its constant rate, takes more than 5 minutes to wrap 60 pieces of candy.

(2) Machines J and K, working together at their respective constant rates, take 1 minute and 30 seconds to wrap 60 pieces of candy.

5) Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour. 20 minutes later, Charlie leaves the same studio and walks towards the same trailer at a constant rate of C miles per hour along the same route as Buster. Will Buster be closer to the trailer than to the studio when he passes Charlie?

(A) Charlie gets to the trailer in 55 minutes.

(B) Buster gets to the studio at the same time as Charlie gets to the trailer.

6) Working together, Max and Mandy painted the living room in six hours. How long would it have taken for Max to paint the room by himself?

(A) Mandy paints twice as fast as Max does.

(B) If Max had left when the job was half finished, it would have taken Mandy hours 4 1/2 to finish the job by herself.

Answer Key

Problem Solving

  1. D
  2. D
  3. E
  4. E
  5. A
  6. C

Data Sufficiency

  1. C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  2. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  3. E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
  4. B. Statement (2) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  5. B. Statement (2) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  6. D. EACH statement ALONE is sufficient to answer the question asked.

Make sure you check out the event Facebook page to see all the comments that were being exchanged during the live session.

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