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HSPT Math : Word Problems

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Example Questions

Example Question #1 : Rate Problems

Jason is driving across the country. For the first 3 hours, he travels 60 mph. For the next 2 hours he travels 72 mph. Assuming that he has not stopped, what is his average traveling speed in miles per hour?

Possible Answers:

$72\ mph$

$66.7\ mph$

$64.8\ mph$

$63.4\ mph$

Correct answer:

$64.8\ mph$

Explanation:

In the first three hours, he travels 180 miles.

$3\times60=180$

In the next two hours, he travels 144 miles.

$2\times 72=144$

for a total of 324 miles.

180+144=324

Divide by the total number of hours to obtain the average traveling speed.

$\frac{324}{5}=64.8\ mph$

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Example Question #221 : Problem Solving Questions

Tom runs a 100m race in a certain amount of time. If John runs the same race, he takes 2 seconds longer. If John ran at 8m/s, approximately how fast did Tom run?

Possible Answers:

10.5m/s

9.5m/s

11m/s

10m/s

9m/s

Correct answer:

9.5m/s

Explanation:

Tom runs a 100m race in a certain amount of time. If John runs the same race, he takes 2 seconds longer. If John ran at 8m/s, how fast did Tom run?

Let denote the amount of time that it took Tom to run the race. Then it took John x+2 seconds to run the same race going 8m/s. At 8m/s, it takes 12.5 seconds to finish a 100m race. This means it took Tom 10.5 seconds to finish. Running 100m in 10.5 seconds is the same as $100/10.5 \approx 9.5m/s$

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Example Question #2 : How To Do Distance Problems

Find the distance from point (2,3) to point (6,7) .

Possible Answers:

$\sqrt2$

$\frac{5}{2}$

$4\sqrt{2}$

Correct answer:

$4\sqrt{2}$

Explanation:

Write the distance formula.

$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the values of the points into the formula.

$d= \sqrt{(6-2)^2+(7-3)^2}$

$d= \sqrt{(4)^2+(4)^2} = \sqrt{16+16} = \sqrt{32}$

The square root of can be reduced because , a factor of , is a perfect square. 16*2=32 .

Now we have $d=\sqrt{16*2}=4\sqrt{2}$

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Example Question #4 : How To Do Distance Problems

Find the distance between the points (0,2) and (2,0) .

Possible Answers:

$8\sqrt2$

$\sqrt2$

$2\sqrt2$

Correct answer:

$2\sqrt2$

Explanation:

Write the distance formula.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plug in the points.

$D=\sqrt{(2-0)^2+(0-2)^2} = \sqrt{(2)^2+(-2)^2} = \sqrt{4+4} = \sqrt{8}$

$D= 2\sqrt2$

The distance is: $2\sqrt2$

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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?

Possible Answers:

$\frac{4}{15}$

$\frac{15}{4}$

$\frac{2}{15}$

$\frac{15}{2}$

$\frac{12}{5}$

Correct answer:

$\frac{15}{4}$

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.

d=st

The speed can be rewritten as: $\frac{1 \textup{ mile}}{8 \textup{ min}}$

Substitute the speed and time.

$d=(\frac{1 \textup{ mile}}{8 \textup{ min}})(30 \textup{ min}) = \frac{30}{ 8}= \frac{15}{4} \textup{ miles}$

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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?

Possible Answers:

$24 - \frac{D}{14}$

$\frac{D}{24}$

$\frac{D}{14}$

$14 - \frac{D}{24}$

Correct answer:

$\frac{D}{24}$

Explanation:

Mr. Thomas gets 24 miles per gallon, and has driven miles; divide distance by gallons used, and he has used $\frac{D}{24}$ gallons. Since he is refilling his car, he is putting $\frac{D}{24}$ gallons in his car.

Note that the amount of gasoline that the tank will hold is irrelevant to the problem.

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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:

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.

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Example Question #22 : 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 stopped for some breakfast on the way to work?

Possible Answers:

Mr. Chapman

Mr. Palin

Mr. Jones

Mr. Idle

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.

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Example Question #23 : Word Problems

Worker graphs

Six friends work for a company as maintenance staff.

Of the six, which one started out, realized he forgot his briefcase, went back for it, and went to work?

Possible Answers:

Mr. Idle

Mr. Gilliam

Mr. Palin

Mr. Chapman

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.

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Example Question #24 : Word Problems

Worker graphs

Six friends work for a company as maintenance staff.

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. Jones

Mr. Cleese

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.

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HSPT Math : Word Problems

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : Rate Problems

Example Question #221 : Problem Solving Questions

Example Question #2 : How To Do Distance Problems

Example Question #4 : How To Do Distance Problems

Example Question #21 : Word Problems

Example Question #22 : Word Problems

Example Question #24 : Word Problems

Example Question #22 : Word Problems

Example Question #23 : Word Problems

Example Question #24 : Word Problems

All HSPT Math Resources

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