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