GMAT Math : Understanding work problems

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Example Question #11 : Understanding Work Problems

When working at the same constant rate, temporary workers at a company can classify 250 files in a day. How many temporary workers would be needed to classify 1250 files in a day?

Possible Answers:

Correct answer:

Explanation:

All five workers have the same work rate, therefore they all complete an equal portion of the work done. Each worker's rate is:

$\frac{1}{5}\times250=50$

Each worker can then classify 50 files in a day.

To classify 1250 files, the company therefore needs the following number of temporary workers:

$\frac{1250}{50}=25$

Twenty-five workers are needed to classify the 1250 files in a day.

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Example Question #11 : Understanding Work Problems

A large water tank has an inlet pipe that can fill the tank completely in three hours, and a drain that can empty it completely in five hours. On one occasion, two hours after the filling of the tank started, the drain was accidentally opened. The error was not immediately discovered, and the drain was not closed until the tank was completely filled. Which of the following comes closest to the number of hours it took to fill the tank?

Possible Answers:

$5\frac{1}{2}$

$3\frac{1}{2}$

$4\frac{1}{2}$

Correct answer:

$4\frac{1}{2}$

Explanation:

Let be the number of hours it took to fill the tank.

The inlet pipe takes three hours to fill the tank, so it can fill $\frac{1}{3}$ tank in one hour, and $\frac{1}{3} T$ tank in hours.

The drain can empty the tank in five hours, so it can remove $\frac{1}{5}$ tank in one hour; since it started two hours after the filling started, it worked for T-2 hours to empty $\frac{1}{5}\left (T-2 \right )$ tank worth of water.

The work performed by the drain was against that performed by the inlet pipe, so the difference of their results is one tank of water. Therefore, the equation to solve for is

$\frac{1}{3} T- \frac{1}{5}\left (T-2 \right ) = 1$

$\frac{1}{3} T- \frac{1}{5} T+ \frac{2}{5}\right ) = 1$

$\left (\frac{1}{3} - \frac{1}{5} \right )T = 1- \frac{2}{5}\right )$

$\left (\frac{5}{15} - \frac{3}{15} \right )T = \frac{3}{5}$

$\frac{2}{15} T = \frac{3}{5}$

$T = \frac{3}{5} \cdot \frac{15} {2} = \frac{45}{10} = \frac{9}{2} = 4 \frac{1}{2}$

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Example Question #12 : Understanding Work Problems

Bryan and his brother Philip, working together, can paint their father's house in a total of sixteen hours. Bryan, working alone, would take twenty-five hours. Which of the following is closest to the number of hours it would take Philip to paint the house, working alone?

Possible Answers:

Correct answer:

Explanation:

Let be the amount of time it would take for Phillip to paint the house by himself. Then he can paint $\frac{1}{T}$ of a house per hour. Similarly, since Bryan can paint the house by himself in 25 hours, he can paint $\frac{1}{25}$ of the house per hour.

Since the two brothers together paint one house in 16 hours, Bryan's share of the work is to paint $\frac{1}{25} \cdot 16 = \frac{16}{25}$ of one house. Phillip's share of the work is to paint $\frac{1}{T} \cdot 16 = \frac{16}{T}$ of the house. Their shares together add up to one house, so the problem to be solved is

$\frac{16}{T}+ \frac{16}{25}= 1$

$\frac{16}{T}= 1 - \frac{16}{25}$

$\frac{16}{T}= \frac{9}{25}$

Cross-multiply and solve:

$9T = 16 \cdot 25 = 400$

$9T \div 9 = 400 \div 9$

$T = 44 \frac{4}{9}$ hours.

Of the given choices, 45 hours comes closest.

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Example Question #31 : Gmat Quantitative Reasoning

A large water tank has an inlet pipe that can fill the tank completely in two and one-half hours, and a drain that can empty it completely in three and one-half hours. On one occasion, when the tank was being filled, the drain was left open; the drain was not closed until the tank was completely full. Which of the following answers comes closest to the number of hours it took to fill the tank?

Possible Answers:

Correct answer:

Explanation:

Let be the number of hours it took to fill the tank.

The inlet pipe takes $\frac{5}{2}$ hours to fill the tank, so it fills $\frac{2}{5}$ tank per hour. The drain empties the tank in $\frac{7}{2}$ hours, so it empties $\frac{2}{7}$ tank per hour. In hours, the inlet pipe filled $\frac{2}{5}T$ tanks of water, but the drain let out $\frac{2}{7}T$ tanks of water; the one tank of water was the difference of these amounts, so

$\frac{2}{5}T- \frac{2}{7}T = 1$

$\left (\frac{2}{5} - \frac{2}{7} \right )T = 1$

$\left (\frac{14}{35} - \frac{10}{35} \right )T = 1$

$\frac{4}{35} T = 1$

$T = \frac{35}{4} = 8\frac{3}{4}$

This makes 9 hours the correct response.

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Example Question #15 : Work Problems

To the nearest hour, how many hours would it take three koala bears - Stuffy, Fluffy, and Muffy - to eat all of the leaves on Mr. Meany's farm if:

Stuffy can eat all the leaves alone in three times as much time that the three together can eat them;

Fluffy can eat all the leaves alone in four times as much time that the three together can eat them; and,

Muffy can eat all the leaves in twenty-four hours?

Possible Answers:

Correct answer:

Explanation:

Let be the number of hours it takes the three koala bears together to eat the leaves. Then Stuffy can eat the leaves in hours, Fluffy can eat them in hours, and Muffy can eat them in 24 hours. Therefore, in one hour, Stuffy, Fluffy, and Muffy can eat $\frac{1}{3t}$ , $\frac{1}{4t}$ , and $\frac{1}{24}$ of the leaves, respectively, and in hours, Stuffy can eat $\frac{1}{3t} \cdot t= \frac{1}{3}$ of the leaves, Fluffy can eat $\frac{1}{4t} \cdot t= \frac{1}{4}$ of the leaves, and Muffy can eat $\frac{1}{24} t$ of the leaves. Since together they are eating all of the leaves, the sum of the three amounts is one task, so we solve for in the equation:

$\frac{1}{3}+\frac{1}{4}+ \frac{1}{24}t = 1$

$\frac{8}{24}+\frac{6}{24}+ \frac{1}{24}t = 1$

$\frac{14}{24}+ \frac{1}{24}t = 1$

$\frac{1}{24}t = 1 - \frac{14}{24}$

$\frac{1}{24}t = \frac{10}{24}$

$\frac{1}{24}t \cdot 24 =\frac{10}{24}\cdot 24$

t = 10

It takes 10 hours for all three koalas together to eat all the leaves on Mr. Meany's farm.

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Example Question #13 : Work Problems

It takes Samuel thirty minutes to make a notebook cover and forty-five minutes to make a book cover. How many hours will it take Samuel to make thirteen notebook covers and three times as many book covers?

Possible Answers:

$21.45\:hr$

$2145\:hr$

$35.75\:hr$

$6.5\:hr$

$32.50\:hr$

Correct answer:

$35.75\:hr$

Explanation:

To begin, convert minutes to hours for each project.

Notebook Cover: $30\:min\cdot\frac{1 \:hr}{60\:min}=0.5\:hr$

Samuel is making thirteen of these, so we need to multiply the result by thirteen. $13*0.5\:hr=6.5\:hr$ is the amount of time Samuel needs to make thirteen notebook covers.

Book Cover: $45\:min\cdot \frac{1\:hr}{60\:min}=0.75\:hr$

Samuel is making three times as many book covers as he is making notebook covers. 13*3=39 , so he is making book covers.

$39*0.75\:hr=29.25\:hr$

It will take Samuel $29.25\:hr$ to make book covers.

Add up the calculated times to get the total number of hours it will take Samuel to make the given number of notebook covers and book covers:

$6.5+29.25=35.75 \:hr$ . That's almost a full work-week of work!

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Example Question #31 : Problem Solving Questions

Together, Mary and I, can trade stocks at a rate of stocks every minutes. I alone on the other hand can only trade stock every minutes. How fast can Mary trade, alone?

Possible Answers:

$\frac{12}{4}$

$\frac{17}{4}$

$\frac{1}{4}$

$\frac{14}{4}$

$\frac{13}{4}$

Correct answer:

$\frac{13}{4}$

Explanation:

To solve this problem, we need to set up an equation as follows

$M+\frac{1}{2}=\frac{15}{4}$ ,.

is Mary's rate.

By simply manipulating the terms, we end up with

$M=\frac{13}{4}$ , which is the final answer.

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Example Question #11 : Work Problems

A doughnut factory has a machine that takes four hours and twenty minutes to make $\textup{1,000 doughnuts}$ . Another machine is brought in that can do the same job in $\textup{two hours and twenty minutes}$ . It is decided to go ahead and allow both machines to work alongside each other until the older machine is worn out.

How long does it take for the $\textup{two machines}$ working together to make $\textup{ 1,000 doughnuts? }$ (Choose the time that is closest to the actual time.)

Possible Answers:

$\textup{1 hour and 15 minutes}$

$\textup{1 hour}$

$\textup{2 hours}$

$\textup{1 hour and 30 minutes}$

$\textup{1 hour and 45 minutes}$

Correct answer:

$\textup{1 hour and 30 minutes}$

Explanation:

The first machine can make $\textup{1,000 doughnuts in 4 hours and 20 minutes, or 260 minutes}$ ; this is

$\frac{1,000}{260} = \frac{50}{13}$ doughnuts per minute.

Similarly, the second machine can make $\textup{1,000 doughnuts in 2 hours and 20 minutes, or 140 minutes}$ ; this is

$\frac{1,000}{140} = \frac{50}{7}$ doughnuts per minute.

Working together, the machines make

$\frac{50}{13} + \frac{50}{7} = \frac{50 \cdot 7 }{13 \cdot 7 } + \frac{13 \cdot 50}{13 \cdot 7} = \frac{350}{91}+ \frac{650}{91} = \frac{1,000}{91}$

doughnuts per minute, or, equivalently, $\textup{1,000 doughnuts per 91 minutes}$ .

$\textup{91 minutes is 1 hour and 31 minutes, making the closest choice 1 hour and 30 minutes}$ .

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Example Question #11 : Work Problems

In a subdivision, several houses of uniform size and design need to be painted; there are two crews working together to paint them. Without the second crew, the first crew painted the first house in twelve hours; together, the two crews painted the second house in five hours. The second crew will paint the third house without the first crew; how long should it take them?

Possible Answers:

$7 \;\mathrm{hrs}$

$17 \;\mathrm{hrs}$

$4.3 \;\mathrm{hrs}$

$3.5 \;\mathrm{hrs}$

$8.6 \;\mathrm{hrs}$

Correct answer:

$8.6 \;\mathrm{hrs}$

Explanation:

Let be the amount of time it takes for the second crew to paint a house without the first.

Think of this as a rate problem, with rate being measured in "houses per hour" rather than "hours per house". The first crew alone can paint $\frac{1}{12}$ house per hour; the second alone can paint $\frac{1}{t}$ house per hour; both together can paint $\frac{1}{5}$ house per hour.

We can find the portion of the house each crew does in an amount of time by multiplying its rate in house per hour by the time in hourse elapsed.

$\mathrm{Work }= \mathrm{rate}\; \times \;\mathrm{ time}$

Let's look at what happens when the two crews are working together over five hours, adding their efforts:

$\frac{1}{12} \cdot 5 + \frac{1}{t} \cdot 5 = \frac{1}{5} \cdot 5$

$\frac{5}{12}+ \frac{5}{t} = 1$

$\frac{5}{t} = \frac{7}{12}$

7t = 60

$t=60\div7\approx 8.6$

The third house will be painted in about 8.6 hours.

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Example Question #12 : Understanding Work Problems

If a triangular field has a base of and a height of , and a garden is taking up 40% of the field. What is the area of the garden?

Possible Answers:

Correct answer:

Explanation:

First, find the area of the triangular field:

A=0.5*b*h

A=0.5*10*5

A=25

The garden takes up 40% of the field, therefore:

Area of garden= $40\%\cdot 25$

Area of garden=

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GMAT Math : Understanding work problems

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #11 : Understanding Work Problems

Example Question #11 : Understanding Work Problems

Example Question #12 : Understanding Work Problems

Example Question #31 : Gmat Quantitative Reasoning

Example Question #15 : Work Problems

Example Question #13 : Work Problems

Example Question #31 : Problem Solving Questions

Example Question #11 : Work Problems

Example Question #11 : Work Problems

Example Question #12 : Understanding Work Problems

All GMAT Math Resources

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