HSPT Math : How to do work problems
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Example Questions
Example Question #1 : Word Problems
Steve can paint his greenhouse in four hours working alone; his ten-year-old son can paint the greenhouse alone in nine hours. Working together, how long, to the nearest minute, would it take them?
Two hours and forty-six minutes
Three hours and six minutes
Three hours and twenty-six minutes
Three hours
Two hours
Two hours and forty-six minutes
Think of these work rates as "greenhouses per hour", not "hours per greenhouse". Then Steve's work rate is one fourth of a greenhouse per hour, and his son's is one ninth of a greenhouse per hour. Now, multiply each rate by the time 
or
This is two hours and forty-six minutes.
Example Question #1 : Word Problems
John and Tom are farmers. John can produce 
John can produce 
Tom can produce 
Example Question #441 : Problem Solving
Tom works in a mall and sells shoes. His monthly salary is 
Let 
Then we can set up the following equation:
Now we solve the equation for 
Example Question #4 : Word Problems
John sells cloths. His monthly salary is 
In order to find how much he makes from selling the cloths, we first multiply the number of cloths sold by 
Now we add his monthly salary:
Example Question #1 : Word Problems
Machine A can produce 4 books in 2 days. Machine B can produce 20 books in 4 days. How many books can machines A and B, working together, produce in 40 days?
200
960
10
120
280
280
Through simplification, we can see that machine A produces 2 books a day and that machine B produces 5 books a day. If we multily each by 40 days and add them together, we find that together they can produce 280 books in 40 days:
Example Question #2 : How To Do Work Problems
Julie sells cars. She has a monthly salary of $1000 and a commission of $500 for each car sold. How much money will she make this month if she sells 7 cars?
$1500
$7000
$4500
$3500
$8000
$4500
To find out how much Julie makes from selling the cars, we first multiply the 7 cars she sells by the $500 that she receives for each car. This gives us $3,500. We now add the $1,000 that she gets for her monthly salary for a total of $4,500.
Example Question #1 : Word Problems
Bob gets paid 
You first calculate how much he makes for normal hours, which is the number of hours works multiplied by the wage. So for normal hours, 
Example Question #1 : Word Problems
A bakery has a machine that can make two hundred loaves of bread in one hour, and a machine that can make three hundred loaves of bread in one hour. How many hours will it take for the two machines together to make 10,000 loaves of bread?
In one hour, the two machines can make a total of
loaves of bread.
Divide 10,000 loaves by 500 loaves per hour:
Example Question #442 : Problem Solving
A candymaker has two machines. One can turn out one hundred pieces of divinity in one hour; the other, an older machine, can do the same in one hour and twenty minutes. Working together and starting at the same time, how many hours would it take for them to make 10,000 pieces of divinity?
Choose the closest answer.
The newer machine can make 100 pieces of divinity per hour. The older machine makes 100 pieces in one hour twenty minutes, or, equivalently, one and one third hours, which is
Together, the machines make 
Divide 10,000 pieces by 175 pieces per hour:
The candy can be made in a little over 57 hours. The closest choice is therefore 60 hours.
Example Question #9 : Word Problems
A candymaker specializes in making "turtles" (pecan caramel candies). She has two machines - a newer machine, which can make one hundred turtles in seventy minutes, and an older machine, which can make one hundred turtles in ninety minutes.
She wants to make one hundred boxes of turtles, each of which holds forty turtles. How many hours would it take for both machines, working together, to produce enough turtles to fill those boxes?
Choose the closest answer.
The newer machine makes one hundred turtles in seventy minutes, or, on the average,
Similarly, the older machine makes, on the average,
Together, they make an average of
turtles per minute.
The candymaker wants one hundred boxes, each with forty turtles, so she wants
multiply this by 
The process takes just over 26 hours; the response closest to the correct time is 25 hours.
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