HSPT Math : How to do work problems

Study concepts, example questions & explanations for HSPT Math

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Example Questions

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Example Question #11 : How To Do Work Problems

A machine can make one hundred caramel creams in twenty five minutes. 

The owner of the machine wants to fill an order of two hundred boxes of caramel creams; eighty of the boxes are to be large boxes, which contain fifty candies each, and the rest are to be small boxes, which contain thirty candies each. How many hours will it take to make enough candies to fill all two hundred boxes?

Select the closest answer.

Possible Answers:

Correct answer:

Explanation:

80 boxes contain 50 candies each; 120 boxes contain 30 candies each. Therefore, there will be a total of 

candies in the boxes.

It takes 25 minutes to produce 100 candies. It takes 

minutes to produce 7,600 candies. Divide by 60 to convert to hours: 

This is 31 hours and 40 minutes. The closest response to this is 30 hours.

Example Question #11 : How To Do Work Problems

Phillip can paint his father's greenhouse in six hours, working alone. His brother Greg can perform the same task in  hours. If the two work together, how many hours, in terms of , does it take them to complete the task?

Possible Answers:

Correct answer:

Explanation:

Phillip can paint the greenhouse in six hours, so he can paint  of the greenhouse in one hour. Likewise, Greg can paint the greenhouse in  hours, so he can paint  of the greenhouse in one hour. 

Working together, they can paint 

of the greenhouse in one hour. Take the reciprocal of this; it takes them

hours to paint the enitre greenhouse, working together.

Example Question #12 : How To Do Work Problems

Kelly can paint her father's shed in five hours, working alone. Working together, she and her sister Sharon can complete the task in hours. In terms of , how many hours would it take for Sharon to complete this task?

Possible Answers:

Correct answer:

Explanation:

Let be the number of hours it would take Sharon to paint the shed alone. Kelly alone can paint the shed in hours, so she can paint of a shed per hour. Similarly, Sharon alone can paint shed per hour, so, working together, they can paint

shed per hour.

Since it takes them five hours to paint the shed together, they can paint shed per hour, so

Take the reciprocal of both expressions:

, the correct choice.

Example Question #11 : How To Do Work Problems

What information in the following word problem is not relevant to the questions?

Jess has a square garden with a length of 5 feet in which there are four kinds of flowers. There are ten tulips, three roses, four petunias, and three lilies. What is the probability of picking a tulip?

Possible Answers:

The side length and of the garden and the shape of the garden.

Four petunias

Three roses

Ten tulips

Three lilies

Correct answer:

The side length and of the garden and the shape of the garden.

Explanation:

For this problem, first identify what the question is asking for.

"What is the probability of picking a tulip?"

Next, identify what is given.

   Shape of the garden: Square

   Length of the garden: 5 feet

   # of tulips: 10

   # of roses: 3

   # of petunias: 4

   # of lilies: 3

Now, identify what is needed to solve the question.

Since you are looking for the probability of picking a flower, you only need the number of the different kinds of flowers and the total number of flowers to get that answer.

From here, find which information that is given is not being used to solve the question.

The side length and of the garden and the shape of the garden would not help find that probability.  

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