Distance, Rate and Time
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Transcript of Distance, Rate and Time
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Distance FormulaSolve for d, r or t
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When are your shoes going to arrive in
Long Beach?
As long as you know the distance and the rate of speed for the ship you can figure
out when the shoes are expected!
You are shipping a container (2 TEUs) of 30,000 athletic shoes from Hong Kong to Long Beach.
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Objective
Today we are going to learn how to apply the distance formula to find distance traveled, time traveled, or rate (speed).
CA Math Content StandardAlgebra and Functions6 2.3 Solve problems involving rates,
average speed, distance, and time.
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Purpose
• Tests and Quizzes• Next Year’s Math Class• Real life applications
• Shipping industry• Travel industry• Trip/Vacation planning
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Distance Formula
Distance = Rate ● TimeDistance
d
Feet, ft Miles Yards Inches, in Meters, m
Kilometers, km Centimeters, cm
Nautical Mile (≈1.15 miles)
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Distance = Rate ● Time
d =
Miles per Hour, mph, miles hour
Kilometers per hourMeters per minute
Nautical Miles per Hour =Knot
Rate
r
Distance Formula
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Distance = Rate ● Time
d = r ● Hours Days Seconds Years
Week Minutes
Time
t
d = rtd = rt Memorize!!!
Distance Formula
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Tell Your Neighbor
• Determine which partner will be person A and which is person B.
• Person A: Tell your partner what r stands for and an example unit.
• Person B: Tell your partner he or she is correct, or tell your partner the correct meaning of r.
r = rate mph, km per hour, …
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Tell Your Neighbor
• Person B: Tell your partner what t stands for and an example unit.
• Person A: Tell your partner he or she is correct, or tell your partner the correct meaning of t.
t = time hour, week, …
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Tell Your Neighbor
• Person A: Tell your partner what d stands for and an example unit.
• Person B: Tell your partner he or she is correct, or tell your partner the correct meaning of d.
d = distance miles, kilometers, …
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Tell Your Neighbor
• Person B: Tell your partner the distance formula.
• Person A: Tell your partner he or she is correct, or tell your partner the correct formula.
Distance Formula
distance = rate ● time
d = r●t d = rt
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Find Distance
If you are traveling for 3 hours at 65 mph, how far will you have gone?
1.Write Down Formula d = rt
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Find Distance
If you are traveling for 3 hours at 65 mph, how far will you have gone?
1.Write Down Formula
2. What are you trying to find AND what do you know?
d = rt
Distance = ??? = dr = 65 mpht = 3 hours
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Find Distance
If you are traveling for 3 hours at 65 mph, how far will you have gone?
1.Write Down Formula
2. What are you trying to find AND what do you know?
3.Substitute known variables and solve
d = rt
Distance = ??? = dr = 65 mpht = 3 hours
d = 65 miles●3 hour hourd = 195 miles
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Person A: Tell Your neighbor the distance formula.
Person B: Correct? Tell your neighbor the rate.
Person A: Correct? Tell your neighbor the time.
Person B: Correct? Explain how to find the distance.
Person A: Correct?
d = rt
r = 55 mph
t = 4 hours
Substitute r and t in formula and solve
If you are traveling for 4 hours at 55 mph, how far will you travel?
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Time to Practice
• I will give you a problem.
• First, you will solve it on your own.
• Second, you will check your solution with your group members.
• Third, I will select one person at random to teach the class how to solve the problem.
• Be sure to refer to your notes for the 3 steps.
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On Your Own
You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
Solve Using Distance Formula:
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Check with your group members
You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
Teach anyone who needs help.
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One person teaches
You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
I will select one person to teach the class
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Solution
You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
d = rtd = 35 miles ● 2 hour
hour
d = 70 miles
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Practice
1.Write Down Formula d = rt
The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day. How far is The Glory Sanye traveling?
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Practice
The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day. How far is The Glory Sanye traveling?
1.Write Down Formula
2. What are you trying to find AND what do you know?
d = rt
Distance = ??? = dr = 480 miles per dayt = 15 days
How far480 miles per day
15 days
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The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day. How far is The Glory Sanye traveling?
1.Write Down Formula
2. What are you trying to find AND what do you know?
3.Substitute known variables and solve
d = rt
Distance = ??? =dr = 480 miles per dayt = 15 days
d = 480 miles ●15 day dayd = 7200 miles
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Time to Practice
• I will give you a problem.
• First, you will solve it on your own.
• Second, you will check your solution with your group members.
• Third, I will select one person at random to teach the class how to solve the problem.
• Be sure to refer to your notes for the 3 steps.
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On Your Own
Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
Solve Using Distance Formula
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Check with your group members
Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
Teach anyone who needs help
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One person teaches
Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
I will select one person to teach the class.
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SolutionNow, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
d = rtd = 520 miles ● 7 day
day
d = 3640 miles
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Nautical Mile
• Distance unit used by ships
• Also used by aviation (air travel)
• Historically equal to 1 min. latitude from the equator
• About 1.15 miles or equal to 1.853 km
• Abbreviate nm
• 1 knot = 1 nm per hour 1 knot = 1 nm per hour or about 1.15 miles per or about 1.15 miles per hourhour
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Tell Your Neighbor• Person B: Tell your neighbor the
abbreviation for nautical mile.
• Person A: Correct? Tell your neighbor how many miles is 1 nautical mile.
• Person B: Correct? Tell your neighbor who uses nautical miles.
• Person A: Correct? Tell your neighbor what a knot is.
• Person B: Correct?
nm
1.15 miles
ships and airplanes
nautical miles per hour
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Find Rate
The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling?1.Write down the distance
formula
d = rt
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Find Rate
The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling?
1.Write down the distance formula
2.What are you looking for and what do you know?
d = rt
rate = ??? = r
d = 13,200 nm
t = 600 hour
How fast
13,200 nautical miles600 hours
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The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling?1.Write down the distance
formula
2.What are you looking for and what do you know?
3.Substitute and solve for rate
d = rtrate = ??? = r
d = 13,200 nm
t = 600 hour13, 200 nm = r ● 600 hour 600 hour 600 hour22 nm/hour = r OR 22 knots = r
Solve Solve for rfor r
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Tell Your NeighborThe MSC Texas is traveling back to Hong Kong, but only a third of the containers are full. It will take the MSC Texas about 15 days to travel 12,500 kilometers to Hong Kong. How fast is the MSC Texas traveling on its return trip?
Partner A: What are you trying to find?
Partner B: Correct? What is the time?
Partner A: Correct? What is the distance?
Partner B: Correct? Explain how you would solve for the rate.
rate or speed
15 days
12,500 km
Substitute distance and time and solve for r
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Time to Practice• I will give you a problem.
• First, you will solve it on your own.
• Second, you will check your solution with your group members.
• Third, I will select one person at random to teach the class how to solve the problem.
• Be sure to refer to your notes for the 3 steps.
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On Your Own
The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
Solve Using Distance Formula:
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Check with your group members
The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
Teach anyone who needs help
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One person teaches
The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
I will select one person to teach the class
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Solution
d = rt
13,200 nm = r ● 550 hour
13,200 nm = r ● 550 hour 550 hour 550 hour
24 nm/hour = r OR 24 knots = r
The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
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Find Time
A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph, how long will it take to reach Sacramento?
1.Write down the distance formula
d = rtd = rt
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Find Time
A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph, how long will it take to reach Sacramento?
1.Write down the distance formula
2.What are you trying to find AND What do you know
d = rttime = ??? = t
d = 375 miles
r = 30 mph = 30
how long375 miles
mileshour
30 mph
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Find TimeA cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph, how long will it take to reach Sacramento?
1.Write down the distance formula
2.What are you trying to find AND What do you know
3.Substitute and solve for t
d = rttime = ??? = t
d = 375 miles
r = 30 mph = 30
375 miles = 30 ● t 30 30
mileshour
mileshour
mileshour
Solve for t
mileshour
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Find Time
A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph, how long will it take to reach Sacramento?
1.Write down the distance formula
2.What are you trying to find AND What do you know
3.Substitute and solve for t
d = rttime = ??? = t
d = 375 miles
r = 30 mph
375 miles = 30 ● t 30 30
12.5 hours = t OR
12 ½ hours
mileshour
mileshour
mileshour
hour
milesmiles
hourmilesmiles
miles
hour miles
hour
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Tell Your NeighborThe new speed trains that the State of California is looking to buy can travel 100 mph. How long would a trip from LA to Sacramento, about 375 miles, take in the new trains?
Partner B: What are you trying to find?
Partner A: Correct? What is the rate?
Partner B: Correct? What is the distance?
Partner A: Correct? Explain how you would solve for the time.
Partner B: Correct?
time
100 mph
375 miles
Substitute distance and rate and solve for t
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Time to Practice
• I will give you a couple problems.
• First, you will solve them on your own.
• Second, you will check your solutions with your group members.
• Third, I will select one person at random to teach the class how to solve each problem.
• Be sure to refer to your notes for the 3 steps.
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Alameda Corridor
Click the picture to see 4 minute clip
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On Your Own
1. In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street?
2. Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda?
Solve Using Distance Formula
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Check with your group members
1. In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street?
2. Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda?
Teach anyone who needs help
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One person teaches
1. In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street?
I will select one person to teach the class
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Solution
d =rt
20 miles = 10 miles/hour ● t20 miles = 10 miles/hour ● t10 miles/hour 10 miles/hour
2 hours = t
1. In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street?
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One person teaches
2. Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda?
I will select one person to teach the class
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Solution
d =rt
20 miles = 40 miles/hour ● t20 miles = 40 miles/hour ● t40miles/hour 40 miles/hour
0.5 hour = t OROR
½ hour = t
2. Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda?
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Summarize in your notes the steps for applying the distance formula to find:
1. Distance
2. Rate
3. Time
Closure