Average Speed

Average Speed

I can...

• Solve unit rate problems using constant speed.

• Solve constant rate problems using the distance formula.

• Solve word problems using rates.

Standards

• 6.NS.10 Use reasoning involving rates and ratios to model real-world and other mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

• 6.NS.8 Interpret, model, and use ratios to show the relative sizes of two quantities. Describe how a ratio shows the relationship between two quantities. Use the following notations: a/b, a to b, a:b.

• 6.NS.9

  Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship.

Fill in the Blanks

Do you remember how to solve equations in the form px = q? Review with a Quick Check.
What is the solution of this equation?

 $6d=108$   $Solve\ for\ d$  

Speed

A speed is a unit rate that can help you solve problems about distance, time, and rate. You can determine distances by using a rate table or by using the distance formula.

What is speed?

• When you hear the word speed, you may think of how fast something is going. Speed is a special type of unit rate.

• The first quantity in the rate is a distance. The second quantity in the rate is a unit of time. For example, a speed of 50 miles per hour can be written as the unit rate  $\frac{50\ mi}{1h}$  , 50mi/h, or 50mph

M'Kynli walks 300 meters every 5 minutes. Complete the rate table.

• What is the unit rate?

• Each column increases by 5 so you can just multiply by 5 or multiply the time by the unit rate.

Ben bikes 3.25 miles every 15 minutes. Complete the rate table.

• Find the unit rate.  $\left(3.25\ \div0.25\right)$  

• Multiply each time in the table by the rate. 

Speed Formulas

• A speed, or rate r, is the ratio of distance, d, to time, t. You can write this relationship as an equation: $r=\frac{d}{t}$  

• For a moving object traveling a distance d at rate (speed) r for time t: distance = rate multiplied by time or  $d=rt$  

The Distance Formula

• Find the distance. r = 14 ft/s, t = 40s

• Write the distance formula d=rt 

• Substitute  $d=14\ \frac{ft}{s}\cdot40s$  (the units of seconds divide out , leaving the unit of feet)

•  $d=14\cdot40ft\ \ \$  

•  $d=560ft$  

Multiple Choice

Which variable represents speed?

• d

• r

• t

Find the time.  $d=\ 348\ \ r=60kmph$  

• Write the distance formula -  $d=rt$ 
  

• substitute   $348km=60kmph\cdot t$  
  

• Isolate the variable  $348kn\div\frac{60km}{1h}=t$   
  

• multiply the recipricol  $348km\cdot\frac{1h}{60km}=t\ \ or\ \ \frac{348km}{1}\cdot\frac{1h}{60km}=t$  

•  $\frac{348}{1}\cdot\frac{1}{60}h=\frac{348}{60}h=t\ or\ 348\div60=t$  

Fill in the Blanks

Jaylen and his family went to visit his aunt. She lives 255 miles away. Assuming the drove at a constant rate, how fast did they travel?

Use mph to label the answer.

The Welch's sailed 30km in 6 hours, stopped for lunch, then sailed 15 km in 5 hours.

What was their average speed? Work on it in groups.

Multiple Choice

Which expression shows how to calculate the speed in meters per second of an object that travels a distance of 60 m every 15 s?

• $60\cdot15$

• $15\div60$

• $60\div15$

• $60\ +15$

Multiple Choice

How long will it take to travel 36mi at a rate of 6 mi/h?

• 6 h

• 42h

• 216 h

• 6 mi

Multiple Choice

Zariah bikes for 3 hours. She covers a distance of 33 miles. Assuming she bikes at a constant rate, how fast was Zariah biking?

• 99 mph

• 11 mph

• 36mph

• 10 mph

Review

• A speed is a unit rate

• It is written as a distance peran amoutn of time like mph, or m/s

• The formula is d=rt, or

   $r=\frac{d}{t},\ \left(r\ =\ d\div t\right)$  

iReady

10 minutes of practice.

Poll

How are you feeling about finding average speed?

• I can do this. No problem!

• I think I've got this with a bit of practice.

• I will need more help to get this.

• I have no idea how to do this.

iReady

10 minutes of practice.