HSPT Math : How to do distance problems

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #11 : How To Do Distance 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?

Possible Answers:

Correct answer:

Explanation:

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 #12 : How To Do Distance 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?

Possible Answers:

Correct answer:

Explanation:

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 #13 : How To Do Distance 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:

Possible Answers:

Correct answer:

Explanation:

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 #14 : How To Do Distance Problems

Worker graphs

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?

Possible Answers:

Mr. Jones

Mr. Idle

Mr. Palin

Mr. Chapman

Correct answer:

Mr. Chapman

Explanation:

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 #15 : How To Do Distance Problems

Worker graphs

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?

Possible Answers:

Mr. Gilliam

Mr. Chapman

Mr. Palin

Mr. Idle

Correct answer:

Mr. Idle

Explanation:

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 #16 : How To Do Distance Problems

Worker graphs

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?

Possible Answers:

Mr. Palin

Mr. Gilliam

Mr. Cleese

Mr. Jones

Correct answer:

Mr. Palin

Explanation:

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 #31 : Word Problems

Worker graphs

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?

Possible Answers:

Mr. Palin

Mr. Chapman

Mr. Gilliam

Mr. Cleese

Correct answer:

Mr. Gilliam

Explanation:

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 #32 : Word Problems

Worker graphs

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?

Possible Answers:

Mr. Cleese

Mr. Palin

Mr. Chapman

Mr. Jones

Correct answer:

Mr. Cleese

Explanation:

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 #471 : Problem Solving

Worker graphs

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?

Possible Answers:

Mr. Cleese

Mr. Jones

Mr. Gilliam

Mr. Palin

Correct answer:

Mr. Jones

Explanation:

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?

Possible Answers:

Correct answer:

Explanation:

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

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