Post on 20-Jan-2016
Warm-up Date 11/13/08Sec 3-5 Proportions and Similar Figures
1) In the figure below, . Find .ABC DEF DF
2) A boy who is 5.5 feet tall casts a shadow that is 8.25 feet long. The tree next to him casts a shadow that is 18
feet long. How tall is the tree?
3) The scale on a map is 1 in. : 20 mi. What is the actual distance between two towns that are 3.5 inches apart on
the map?
about 19.7 cm
12 ft
70 mi
Date 11/20/08
Sec 3-6
Equations and
Problem Solving
Goal:x To define a variable in terms of another variable
x To model distance-rate-time problems
…And WhyTo solve real-world problems involving
distance, rate, and time, as in examples 3-5
Key Words:consecutive integers:
Numbers that differ by 1.Example: 50 and 51
10, 9, and 8
uniform motion:An object that moves at a constant rate.
The formula gives the relationship between distance , rate , and time .
d rtd r t
The width of a rectangle is 3 in. less than its length. The perimeter of the rectangle is 26
in. What is the width of the rectangle?
Perimeter = 26 in.
P 26 Lenght:Width:
x3x
x
x
3x 3x
x 3x x 3x 264x 6 26
4 6 26x 6 6
4x32 4 4 x 8
85
The width of the rectangle is 5
The sum of three consecutive integers is 72. Find the integers.
1st Integer:2nd Integer:
3rd Integer:
x1x 2x
x 1x 2x 723 3x 72
3 3 3x 69 3 3 x 23
232425
An airplane left an airport flying at 180 mi/h. A jet that flies at 330 mi/h left 1 hour later. The jet follows the same
route as the airplane at a different altitude. How many hours will it take the jet to catch up with the airplane?
1st plane:
2nd plane:
x1x
d rt
180x 330 1x 180x330x 330330 330x x 150x 330
150 150 x 1
2 hours5
Therefore it will take the jet 1
hours to catch up to the 1st plane.
Suppose you hike up a hill at 4 km/h. You hike back down at 6 km/h. Your hiking trip took 3 hours. How
much time did it take you to hike up the hill?
up hill:
down hill:
x3 x
d rt4x 6 3 x 4x18 6x6 6x x
10x18 10 10 x 1.8 hr
It took 1.8 hours to hike up the hill.
Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 50 mi/h faster that the other.
After two hours, the jets are 2500 miles apart. Find the speed of each jet.
1st jet:
2nd jet:
x50x
d rt2 hourst
2500 milesd
2500 2x 2 50x 2500 2x 2 100x 2500 4 100x 100 100 2400 4x
4 4 x600
The first jet was traveling at 600 mi/h
and the second jet was traveling at 650 mi/h.
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Planner:x Write today’s goal.
x Write today’s assignment.
Assignment:x Pg 162
2 – 18 e, 28, 36 – 42 e
x Reflective Journal