All HSPT Math Resources
Example Questions
Example Question #11 : Word 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.
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 : Word 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?
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 : Word 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?
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?
Four petunias
The side length and of the garden and the shape of the garden.
Three roses
Three lilies
Ten tulips
The side length and of the garden and the shape of the garden.
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.
Example Question #13 : Word Problems
Kate and Bella were both travelling at the same speed. Kate went 300 miles in 5 hours. Bella travelled 450 miles. How many hours did it take for Bella to reach her destination?
The distance formula is essential in this problem.
First, use Kate's info to figure out the rate for both girls since they're travelling at the same speed, which is . Then, plug in that rate to the formula with Bella's information, which gives her a time of hours.
Example Question #14 : Word Problems
Joe drove an average of 45 miles per hour along a 60-mile stretch of highway, then an average of 60 miles per hour along a 30-mile stretch of highway. What was his average speed, to the nearest mile per hour?
At 45 mph, Joe drove 60 miles in hours.
At 60 mph, he drove 30 miles in hours.
He made the 90-mile trip in hours, so divide 90 by to get the average speed in mph:
Example Question #3 : Number Concepts And Operations
1 mile = 5280 feet
If Greg's house is 5.3 miles away, how far is it in feet?
Using the conversion formula, you would multiply 5.3 miles by 5280 feet and you will get 27,984 feet.
Example Question #455 : Problem Solving
Sophie travels f miles in g hours. She must drive another 30 miles at the same rate. Find the total number of hours, in terms of f and g, that the trip will take.
g + f
g + f + 30
Using d = rt, we know that first part of the trip can be represented by f = rg. The second part of the trip can be represented by 30 = rx, where x is some unknown number of hours. Note that the rate r is in both equations because Sophie is traveling at the same rate as mentioned in the problem.
Solve each equation for the time (g in equation 1, x in equation 2).
g = f/r
x = 30/r
The total time is the sum of these two times
Note that, from equation 1, r = f/g, so
=
Example Question #456 : Problem Solving
Gary is the getaway driver in a bank robbery. When Gary leaves the bank at 3 PM, he is going 60 mph, but the police officers are 10 miles behind traveling at 80 mph. When will the officers catch up to Gary?
3:10 PM
4:00 PM
5:00 PM
3:30 PM
4:45 PM
3:30 PM
Traveling 20 mph faster than Gary, it will take the officers 30 minutes to catch up to Gary. The answer is 3:30 PM.
Example Question #3 : How To Do Distance Problems
Trevor took a road trip in his new VW Beetle. His car averages 32 miles per gallon. Gas costs $4.19 per gallon on average for the whole trip. How much would it coust to drive 3,152 miles?
To find this answer just do total miles divided by miles per gallon in order to find how many gallons of gas it will take to get from point A to Point B. Then multiply that answer by the cost of gasoline per gallon to find total amount spent on gasoline.