All HSPT Math Resources
Example Questions
Example Question #21 : Word Problems
Suppose a student ran a pace of eight minutes per mile at consistent pace. He arrived at the school in thirty minutes. How far is the school in miles?
The consistent pacing tells us that this is a linear relationship between distance and the student's speed and time.
Write the equation for the distance travelled.
The speed can be rewritten as:
Substitute the speed and time.
Example Question #22 : Word Problems
Mr. Thomas's car holds exactly 14 gallons of gasoline, and gets 24 miles per gallon. He gets into his car, which has a full gas tank, and drives miles. He then refills the car until the gas gauge reads "full" again. In terms of , how many gallons of gasoline did he put in his car?
Mr. Thomas gets 24 miles per gallon, and has driven miles; divide distance by gallons used, and he has used gallons. Since he is refilling his car, he is putting gallons in his car.
Note that the amount of gasoline that the tank will hold is irrelevant to the problem.
Example Question #24 : Word Problems
Mrs. Williams' car gets miles to the gallon; its tank holds gallons. Mrs. Williams gets into her car, which has a full tank; she drives miles, and then refills the tank completely with gasoline that costs dollars per gallon.
In order to determine the amount Mrs. Williams paid for the gasoline, you need to know the value of each of the following varables except:
The price of the gasoline Mrs. Williams purchased is the number of gallons multiplied by the price per gallon. is the latter quantity, so it is needed to answer the question.
To find the amount of gasoline purchased - which is the amount she used - it is necessary to divide the number of miles she drove by the gas mileage in miles per gallon. These are and , so both are needed to answer the question.
is not relevant to the problem, and is the correct choice.
Example Question #22 : Word Problems
Six friends work for a company as maintenance staff.
Above are six graphs. Each graph shows the distance that one of the six is from his home from 8 AM to 9 AM on a particular day, relative to the time. The time of day is represented by the horizontal axis, and the distance from home is represented by the vertical axis. The name of the person represented by each graph is under the graph.
Of the six, who stopped for some breakfast on the way to work?
Mr. Idle
Mr. Palin
Mr. Chapman
Mr. Jones
Mr. Chapman
We are looking for someone whose distance from home increased steadily for a while, then became constant (since the person had to have not been moving), then increased steadily again. This describes the graph for Mr. Chapman.
Example Question #462 : Problem Solving
Six friends work for a company as maintenance staff.
Above are six graphs. Each graph shows the distance that one of the six is from his home from 8 AM to 9 AM on a particular day, relative to the time. The time of day is represented by the horizontal axis, and the distance from home is represented by the vertical axis. The name of the person represented by each graph is under the graph.
Of the six, which one started out, realized he forgot his briefcase, went back for it, and went to work?
Mr. Chapman
Mr. Gilliam
Mr. Idle
Mr. Palin
Mr. Idle
The distance this person was from his home increased steadily as he went to work, then decreased as he went back home for his briefcase, then increased again as he went on to work. This describes the graph for Mr. Idle.
Example Question #463 : Problem Solving
Six friends work for a company as maintenance staff.
Above are six graphs. Each graph shows the distance that one of the six is from his home from 8 AM to 9 AM on a particular day, relative to the time. The time of day is represented by the horizontal axis, and the distance from home is represented by the vertical axis. The name of the person represented by each graph is under the graph.
Of the six, which one works the night shift, and therefore went from work to home between 8 AM and 9 AM?
Mr. Palin
Mr. Gilliam
Mr. Jones
Mr. Cleese
Mr. Palin
Since the person in question went home, his distance from home decreased rather than increased as time went on. The graph will be a falling line; this graph represents Mr. Palin.
Example Question #11 : How To Do Distance Problems
Six friends work for a company as maintenance staff.
Above are six graphs. Each graph shows the distance that one of the six is from his home from 8 AM to 9 AM on a particular day, relative to the time. The time of day is represented by the horizontal axis, and the distance from home is represented by the vertical axis. The name of the person represented by each graph is under the graph.
Of the six, who got halfway there, got sick, and returned home?
Mr. Chapman
Mr. Cleese
Mr. Palin
Mr. Gilliam
Mr. Gilliam
The person's distance increased as he drove to work, but decreased as he returned home. This describes the graph for Mr. Gilliam.
Example Question #12 : How To Do Distance Problems
Six friends work for a company as maintenance staff.
Above are six graphs. Each graph shows the distance that one of the six is from his home from 8 AM to 9 AM on a particular day, relative to the time. The time of day is represented by the horizontal axis, and the distance from home is represented by the vertical axis. The name of the person represented by each graph is under the graph.
Of the six, who took the express train directly to work?
Mr. Palin
Mr. Jones
Mr. Chapman
Mr. Cleese
Mr. Cleese
The distance from home of the worker in question would have increased steadily without any interruption. The graph with the constantly increasing line is the one to choose; this graph belongs to Mr. Cleese.
Example Question #13 : How To Do Distance Problems
Six friends work for a company as maintenance staff.
Above are six graphs. Each graph shows the distance that one of the six is from his home from 8 AM to 9 AM on a particular day, relative to the time. The time of day is represented by the horizontal axis, and the distance from home is represented by the vertical axis. The name of the person represented by each graph is under the graph.
Of the six, which one called in sick at 7:30 AM and stayed in bed?
Mr. Gilliam
Mr. Palin
Mr. Jones
Mr. Cleese
Mr. Jones
Someone who called in sick would remain at constant zero distance from his home during the entire time. This would be represented by a horizontal line along the zero axis; this describes the graph for Mr. Jones.
Example Question #34 : Word Problems
On a map, one half of an inch represents forty miles of real distance.
It takes John 90 minutes to get from Kingsbury to Willoughby driving an average of miles per hour. How many inches apart, in terms of , are the two cities on the map?
The distance in real miles between Kingsbury in Willoughby can be found by multiplying rate miles per hour by time 90 minutes, or one and a half hours:
Let represent map distance between the cities, One half of an inch represents forty miles of real distance, so one inch represents twice this, ir eighty miles. The ratio that compares map distance and real distance is