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