Fish Speeds
A study was conducted comparing the speeds of 2 different fish. Fish A swims at a rate of 3 meters every 2 seconds. Fish B's record the following:
1.6 m. 3.2 m 4.8 m 9.6m
1 sec 3 sec 6 sec 9 sec
Who swims the fastest?
Fish A swims the fastest.
To show a proportional relationship, a line has to pass through ______?
The origin, (0,0)
Where is the error?
Step 1: 5(x-3) +4x = 10x + 4 (x+2)
Step 2: 5x-15 + 4 x = 10x + 4x + 8
Step 3: 9 x - 15 = 14 x +8
Step 4: 23 x = 23
Step 5: x = 1
Step 4- did not subtract 14 x; added instead
Write an equation for a car traveling 60 miles in 2 hours.
y= 30 x
A car travels 180 miles in 3 hours. How far will the car be in 10 hours if traveling at the same speed?
180/3 = 60
y= 60x
y = 60 (10)
y = 600 miles
Based on the table, how do you calculate Fish B’s speed in meters per second?
Seconds 0 1 3 6 9
Meters. 0. 1.6 4.8 9.6. 14.4
Divide meters by seconds.
How can you tell which graph shows the fastest speed?
The line that is the steepest.
Solve the equation:
10- 6/5 x = 8
10/6 or 1 2/3 or 1.666
Set up an equation to find the speed of a car that covers 120 miles in 3 hours. What is the unit rate?
y= 40x
120 miles/ 3 hours = 40 miles/ hour
A train climbs a hill, gaining 400 feet in elevation over a horizontal distance of 8 miles. How many feet in elevation were they at 3 miles?
400/8 = 50
y= 50x
y = 50 (3)
150 feet in elevation
How much slower is Fish B than Fish A?
0.2 meters per second slower
Demonstrate a graph that uses the proportion table:
Time, t (sec) Distance, m (meters0
5 10
10 20
20 40
50 100
Examine Drawings
How do you know when an equation has no solutions?
The variables cancel out leaving 5=6 or something like that.
A hiker climbs a mountain, gaining 600 feet in elevation over a distance of 3 miles. What is the hiker's average rate of elevation gain per mile?
The slope (rate of elevation gain) is the change in elevation divided by the distance traveled:
Slope is 600 ft/ 3 miles or 200 ft per mile
So, the hiker gains elevation at an average rate of 200 feet per mile.
A cyclist rides 12 miles in 1.5 hours. What is the cyclist’s average speed in miles per hour?
12/ 1.5
8 miles/hour
Compare Fish A’s speed and Fish B’s speed. What are their exact speeds?
Fish A 2/3 meters per second or .666 m/s
Fish B 6/10 meters per second or 3/5 m/s or .60 m/s
Show a 20-gallon tank losing 4 gallons every 5 minutes?
Examine Drawings
What are the steps for solving this problem?
5 (x-13) + 5/6x = 20 ( 5x - 15) -80x
Distribute
Combine Like Terms
Solve for X
A cyclist rides up a hill, increasing his altitude by 150 feet over a horizontal distance of 2.5 miles. What is the cyclist's average rate of altitude gain per mile?
150/2.5 = 60 ft. per mile
Plant grows 15 inches in 5 weeks. Plant B grows 22 inches in 7 weeks.What is the average growth for each plant and who grows the quickest?
15/5 = 3 inches/week
22/7 = 3 1/7 inches/week= Plant B
What units are used to measure the speed of Fish A and Fish B?
Meters per second
Create your own graph for a car traveling 100 miles in 2 hours. What does the slope represent?
The slope represents the car’s speed, which is 50 miles per hour.
How do you know when an equation has infinitely many solutions?
John and Sara checked out the same amount of books from Mrs. Squires. John had 5 times the product of 10 less than a number plus 52. Sara had 15 plus 6 times the product of a number minus 3. How many books did they each have?
5 (x-10) + 52 = 15 + 6 (x-3)
5x -50 + 52 = 15 + 6x - 18
5x + 2 = 6x -3
x = 5
They each checked out 5 books
Imagine a car is traveling and losing value over time, such as depreciation. Below is the data:
Time Value
0 20,000
2 12,000
4 4,000
What is the rate of depreciation
20,000-12,000
----------------
2-0
$4,000 per year