Time and Distance Formulas

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Time and Distance Formulas

• Steve Tuckerman
• 11 th Grade Mathematics
• Education page

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What are Time and Distance formulas?

• Time and Distance Formulas relate time, distance,
  and speed. These relationships have many
  practical applications. Right now, Jeff Gordon
  is trying to decide how fast he has to go to pass
  Jimmie Johnson.

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How to get around in this lesson

• There will be a series of buttons to choose from.
  Forward and backward buttons are located on the
  bottom of the slide.
• The home button returns you to the main menu
• Quizzes have answer buttons. Click on the button
  that you think is the right answer. Answer
  buttons look like this

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Main Menu

• Tutorial
• Quiz One Given rate and time, calculate
  distance.
• Quiz Two Given distance and time, calculate
  pace.
• Quiz Three Convert minutes per mile to miles per
  hour.

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Why do you need to know the Time and Distance
Formula?

• To figure how long a trip will take
• To see how far you can go in a set amount of time
• To see how fast you took a trip
• To compare different trips

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Steps in solving Time and Distance Formulas

• Step 1. Translate the question into mathematical
  terms. For example, if you are asked miles per
  hour, write the question as miles divided by
  hours.

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Steps in solving Time and Distance Formulas

• Step 2. Put everything in constant units. For
  example, if the question asks miles per hour,
  every time must be placed in terms of hours, and
  every distance must be placed in terms of miles.

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Conversion Units

• Remember There are 60 seconds in a minute, 60
  minutes in an hour, and 24 hours in a day.
• Remember There are 12 inches in a foot, 3 feet
  in a yard, and 5280 feet in a mile.

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Time Conversions

• To convert minutes to hours, divide by 60.
• To convert hours to minutes, multiply by 60
• To convert seconds to minutes, divide by 60
• To convert minutes to seconds, multiply by 60
• To convert days to hours, multiply by 24
• To convert hours to days, divide by 24

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Measurement Conversions

• To convert inches to feet, divide by 12
• To convert feet to inches, multiply by 12
• To convert feet to miles, divide by 5280
• To convert miles to feet, multiply by 5280

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• Step 3. Write the equation you want to solve.
• Use the correct formula to solve it.
• Be careful about what you multiply, and what you
  divide!

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What are the basic formulas?

• Distance Rate Time (d r t)
• Rate Distance / Time (r d/ t)
• Time Distance / Rate (t d / r)
• Be sure you use the right formula!

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To find distance

• Distance Rate Time (d r t)
• For example, to find miles, multiply miles
  per hour (rate) times the number of hours.
• Miles Miles x Hours
• Hours
• The hours cancel, you are left with miles.

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To find the rate of speed

• Rate Distance / Time (r d/ t)
• To find miles per hour, divide miles driven by
  the number of hours driven.

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To find the time it takes to travel.

• Time Distance / Rate (t d / r)
• Hours Miles_____
• Miles/Hour
• Remember, to divide fractions, flip and multiply
• Hours Miles x Hours
• Miles
• Miles cancel, you are left with hours

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Quiz 1

• How far can you go in 30 minutes at 55 miles per
  hour? Bowser wants to go skiing with his
  friends.

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Step one

• Put in constant units
• Rate was given in miles per hour, so time must be
  in hours
• Remember, to convert minutes to hours, divide by
  60

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Question 1What time should be used?

• We are given 30 minutes. We want the answer in
  hours.
• Answer
• A. 2 hours
• B. 0.5 hours
• C. 30 hours

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• Nice try. Bowsers friends are still waiting.
• Remember, to convert minutes to hours, divide
  by the number of minutes by 60. You divided by
  15.

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• Nice try. Bowsers friends are still waiting. You
  just changed minutes into hours.

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• Nice job! The time is one half hour, or 0.5
  hours. Bowser goes skiing with his friends.

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Question 2

• Now, how do you calculate how far you can go?
• A. Distance 0.5 hours / 55 miles per hour
• B. Distance 0.5 hours times 55 miles per hour
• C. Distance 55 miles / 0.5 hours
• Remember the basic formulas!

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• Nice try. If distance equals rate times time,
  then you must multiply, not divide.
• Distance Rate Time (d r t)

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Question 3

• Well done. You have the formula correct. Distance
  equals rate times time, so distance equals 0.5
  times 55, or 27.5
• 27.5 is in what units?
• A. Hours
• B. Miles
• C. Speed

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• Nice try. Remember, we were talking about miles
  per hour, so the answer is in miles

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• Well done. You can go 27.5 miles in 30 minutes
  traveling at 55 miles per hour.
• Are you ready for another quiz? If so, click the
  right arrow

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Quiz 2

• Joan Benoit won the 1984 Olympic marathon in 2
  hours, 24 minutes, and 52 seconds. If a marathon
  is 26.22 miles, what was her average pace in
  minutes per mile?

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Question 1

• The first step is to put everything in constant
  units. If it took Joan 2 hours, 24 minutes, and
  52 seconds to run her race, and we are interested
  in her pace in minutes per mile, what is our
  first step?
• Place everything in terms of hours
• Place everything in terms of minutes
• Place everything in terms of seconds

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• Nice try. We want to know how many minutes it
  took Joan to run each mile, so we need to know
  how many minutes she was running.

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• Well done. Since we want to know Joans average
  pace in terms of minutes per mile, we need to put
  everything in terms of minutes.

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Question 2

• We know that Joans time was 2 hours, 24 minutes,
  52 seconds. What formula gives us the number of
  minutes?

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• Remember, to convert hours to minutes, multiply
  by 60. To convert seconds to minutes, divide by
  60. Everything has to be in terms of minutes.

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• 2 times 60 plus 24 plus 52
• 2 times 60 plus 24 plus 52/60
• 2 times 60 plus 24 plus 52/100
• Remember, you are converting 2 hours, 24
  minutes, 52 seconds to minutes.

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• Nice try. Remember, we want the answer in
  minutes. To convert hours to minutes, multiply by
  60. To convert seconds to minutes, divide by 60.
  You forgot to convert seconds to minutes.

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• Nice try. Remember, we want the answer in
  minutes. To convert hours to minutes, multiply by
  60. To convert seconds to minutes, divide by 60.
  You divided seconds by 100.

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• Well done. The answer is 2 times 60 plus 24 plus
  52/60. You multiply 2 hours times 60 minutes per
  hour, add the 24 minutes, and add 52 seconds / 60
  seconds in a minute. All units are now in
  minutes. The correct answer is 144.87 minutes

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Question 3

• What was Joans average pace per mile? Remember,
  she ran 26.22 miles in 144.87 minutes.
• 144.87/26.22 5.525, or 5 minutes 31 seconds
  per mile
• 26.22/144.87 .18 minutes per mile

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• Nice try. Remember, we wanted Joans pace in
  minutes per mile. Therefore, you divide the
  number of minutes she was running by the number
  of miles she ran. You did it backwards.

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• Well done. Joans average pace per mile in the
  1984 Olympic marathon was 5 minutes and 31
  seconds per mile. How far can you run at that
  pace? Click the right arrow for the next quiz.

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Quiz 3

• We know that Joan Benoit ran the 26.22 mile
  Olympic marathon at an average pace of 5 minutes
  and 31 seconds per mile. What was her speed in
  miles per hour?

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Step one

• First, we have to put everything in constant
  units. We are interested in miles per hour, so we
  need to convert minutes to hours.

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Question 1How do you convert minutes to hours?

• Multiply the number of minutes by 60
• Divide the number of minutes by 60
• Multiply by 24

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• Nice try. Remember, you have to divide the
  number of minutes by 60. You multiplied by 60.

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• Nice try. You multiplied by 24. You should have
  divided by 60.

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Question 2

• Well done. There are 60 minutes in an hour, so
  you divide the number of minutes by 60.
• How do you convert 5 minutes and 31 seconds into
  hours?

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• A. Divide 5.31 by 60
• B. First convert 31 seconds into minutes, add to
  5, then divide by 60
• C. Multiply 5.31 times 24

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• Nice try. Remember, you need to convert
  everything into minutes, so you have to convert
  seconds into minutes. You forgot to make this
  conversion.

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• Nice try. Remember, you need to convert
  everything to minutes. You tried to convert to
  days.

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Question 3

• Well done. First, convert the 31 seconds into
  minutes. 31/60 .52. Now, add the .52 to 5
  minutes to get 5.52. Then, divide by 60. The
  answer is .092. Joan ran each mile in .092 hours.
  
• How do you convert one mile in .092 hours into
  miles per hour?

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• 1 mile divided by .092 hours equals x miles
  divided by one hour
• Cross multiply 1 mile times 1 hour .092 times
  x miles
• X miles 1/.092
• X 10.9 miles per hour.

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• Congratulations on completing your first lesson
  on time and distance formulas.
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