Solve for : 24 7x x

7 24x

Monday’s Warm Up

717x

7

Objective

By the end of today’s lesson, you will be able to solve an equation for a particular letter, given that the equation contains multiple letters

Example #1

Solve for x Solve for x

24 7x d x p 7 24x

17x

x p d

x d p

Example #2

Solve for t Solve for t

35 5t d rt5 35t

7t

rt d

td

r

Example #3

Solve for l Solve for l

60 5 4l V lwh5 4 60l 20 60l

lwh V

lV

wh3l

Example #4

Solve for b Solve for b

10 3 4b z br p 10 3 4b

3 6b

z pbr pbr z

2b zbr p

r r

b

p z

r

Example #5

Solve for t Solve for t

2 5 35t 2s t r 10 35t

25t 2s rt

2st r

25t 1 1 2t r s

2t r s

Example #6

Solve for p Solve for p

456

p

ph

n

456

p

270p p hn

645 6

1 6

p

ph

n

1

nh n

n

p

Example #7

Solve for r Solve for r

78.5 2 3.14 r 2C r

12.5r 2r

C

6.28 78.5

6.28 6.28

r

2 Cr 2

2 2

Cr

6.28 78.5r

Example #8

Solve for l Solve for l

160 2 2 15l 2 2P l w

65l

2 130l

2 2l w P 2 30 160l 2 2l P w

2

2 2

w Pwl

P

Example #9

Solve for x Solve for x

5 4 3 32x x ax b cx d

2 4 32x

x xa c b d 5 3 4 32x x a c bx d

2 28x 14x

a c dx b

a c d b

a c a c

x

Example #9

Solve for x Solve for x

5 4 3 32x x

2 4 32x 5 3 4 32x x

2 28x 14x

a c d b

a c a c

x

xd b

a c

Example #10

1Solve for b 1Solve for b

112120 5 3b

1 3 48b

112 5 3 120b

12 11 2 5 3 120 2b

15 3 2405 5

b

1 45b

11 22A h b b

12 1 2h Ab b

12 1

21 2 2bh b A 21 2h b Ah h

b 2

21Ahbb

21 2

Ahb b

Motion Problem Set Ups3. Lois rode her bike to visit a friend. She traveled at 10 mi/h. While she was there, it began to rain. Her friend drove her home in a car traveling at 25 mi/h. Lois took 1.5 h longer to go to her friend’s than to return home. How many hours did it take Lois to ride to her friend’s house?

Distance

to by bike

home by

1.510 10

car 25 25

1.5t

Rate Ti

mph

mph

me

t

t t

1.510 25t t

Motion Problem Set Ups4. Fred begins walking toward John’s house at 3 mi/h. John leaves his house at the same time and walks toward Fred’s house on the same path at a rate of 2 mi/h. How long will it be, in minutes, before they meet if the distance between the houses is 4 miles?

Distance

Fred 3 3

J 2 2ohn

t t

Rate

mph

m

ime

ph t

T

t

3 2 4t t

Motion Problem Set Ups5. May rides her bike the same distance that Leah walks. May rides her bike 10 km/h faster than Leah walks. If it takes May 1 h and Leah 3 h to travel that distance, how fast does each travel?

Distanc

10 10

e

Ma

L h 3

y

e

1

3a

r

Rate Ti

hr r

r

m

r

e

hr

0 31r r

Motion Problem Set Ups6. A train leaves the station at 6:00 P.M. traveling west at 80 mi/h. On a parallel track, a second train leaves the station 3 hours later traveling west at 100 mi/h. At what time will the second train catch up with the first?

Distance

First Train

Second Trai

8

3 3

0 80

100 100n

mph t t

t

Rate Time

mph t

80 10 30t t

Motion Problem Set Ups7. At 10:00 A.M., a car leaves a house at a rate of 60 mi/h. At the same time, another car leaves the same house at a rate of 50 mi/h in the opposite direction. At what time will the cars be 330 miles apart?

60

Distance

First Car

Second

60

50Car 50

m

Rate Tim

ph

mph

e

t t

t t

60 50 330t t

Motion Problem Set Ups

8. It takes 1 hour longer to fly to St. Paul at 200 mi/h than it does to return at 250 mi/h. How far away is St. Paul?

Distance

Fly to St. Paul

Rtn from St.

1 120

Paul

0 200

250 250

t

Rate Ti

mph

mp t

m

h t

e

t

1200 250t t

Tuesday Night’s HomeworkSolve Each of today’s worksheet problems

Wednesday Warm UpThe Charlestown Chiefs football team scored 10 times for a total of 46 points. If a touchdown is worth 7 points and a field goal is worth 3 points, how many touchdowns and how many field goals did the Chiefs score?

7 3 10 46x x # of Touchdowns:

# of Field Goals: 0 1

x

x 7 30 3 46x x 4 30 46x

4 16x 4x

# of Touchdowns:

# of Field Goals

4

: 6

Two jets leave Dallas at the same time and fly in opposite

directions. One is flying west 50 mi/h faster than the other.

After 2 hours, they are 2500 miles apart. Find the speed of

each jet.

How are the distances that the two jets fly related

Distance flown by 1st Jet + Distance flown by 2nd jet = 2500 mi

Two jets leave Dallas at the same time and fly in opposite

directions. One is flying west 50 mi/h faster than the other.

After 2 hours, they are 2500 miles apart. Find the speed of

each jet.

How are the times that the two jets fly related

The time of flight of 1st Jet = The time of flight of 2nd Jet

Two jets leave Dallas at the same time and fly in opposite

directions. One is flying west 50 mi/h faster than the other.

After 2 hours, they are 2500 miles apart. Find the speed of

each jet.

How are the speeds of the two jets fly related

Speed of Westbound Jet = Speed of Eastbound Jet + 50 mi/hr

Two jets leave Dallas at the same time and fly in opposite

directions. One is flying west 50 mi/h faster than the other.

After 2 hours, they are 2500 miles apart. Find the speed of

each jet. Define: Let x = the speed of the jet flying east.

Write: 2 x + 2( x + 50 ) = 2500

Then x + 50 = the speed of the jet flying west.

Relate: eastbound jet’s plus westbound jet’s equals the total distance distance distance

Jet Rate Time Distance Traveled

Eastbound x 2 2x

Westbound x + 50 2 2(x + 50)

Eastbound

Westbound

Two jets leave Dallas at the same time and fly in opposite

directions. One is flying west 50 mi/h faster than the other.

After 2 hours, they are 2500 miles apart. Find the speed of

each jet.

Two jets leave Dallas at the same time and fly in opposite

directions. One is flying west 50 mi/h faster than the other.

After 2 hours, they are 2500 miles apart. Find the speed of

each jet.

Jet Rate Time Distance Traveled

Eastbound x 2 2x

Westbound x + 50 2 2(x + 50)

Eastbound

Westbound

Westbound Jet: 650mph Eastbound Jet: 600mph

2 2 100 2500

4 100 2500

4 2400

600

x x

x

x

x mph

1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart?

Rate Time DistanceNorthboundSouthbound

1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart?

Rate Time DistanceNorthbound 83 mphSouthbound 67 mph

1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart?

Rate Time DistanceNorthbound 83 mph tSouthbound 67 mph t

1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart?

Rate Time DistanceNorthbound 83 mph t 83tSouthbound 67 mph t 67t

83 67 600t t

2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet?

Rate Time DistanceRomeoJuliet

2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet?

Rate Time DistanceRomeo 5 m/sJuliet 4 m/s

2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet?

Rate Time DistanceRomeo 5 m/s tJuliet 4 m/s t – 3

2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet?

Rate Time DistanceRomeo 5 m/s t 5tJuliet 4 m/s t – 3 4(t – 3)

5 4 3 87t t

3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?

Rate Time DistanceBad Bart

Police Helo

3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?

Rate Time DistanceBad Bart 70 mph

Police Helo 100 mph

3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?

Rate Time DistanceBad Bart 70 mph t

Police Helo 100 mph t – .5

3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up?

Rate Time DistanceBad Bart 70 mph t 70t

Police Helo 100 mph t – .5 100(t – .5)

70 100 .5t t

4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go?

Rate Time DistanceUphill

Downhill

4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go?

Rate Time DistanceUphill 4 mph

Downhill 20 mph

4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go?

Rate Time DistanceUphill 4 mph t

Downhill 20 mph 3 - t

4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go?

Rate Time DistanceUphill 4 mph t 4t

Downhill 20 mph 3 - t 20(3 - t )

4 20 3t t

Wednesday Night’s Homework

Complete a D = RT table for each problem. Then use the table to construct an equation.

Thursday Warm Up

Solve each of the problems from last night’s homework.

1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart?

Rate Time DistanceCamel #1Camel #2

1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart?

Rate Time DistanceCamel #1 9 km/hrCamel #2 7 km/hr

1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart?

Rate Time DistanceCamel #1 9 km/hr tCamel #2 7 km/hr t

1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart?

Rate Time DistanceCamel #1 9 km/hr t 9tCamel #2 7 km/hr t 7t

9 7 60t t

2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel.

Rate Time DistanceCamel #1Camel #2

2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel.

Rate Time DistanceCamel #1 r km/hrCamel #2 (r + 3)km/hr

2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel.

Rate Time DistanceCamel #1 r km/hr 4 hrCamel #2 (r + 3)km/hr 4 hr

2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel.

Rate Time DistanceCamel #1 r km/hr 4 hr 4rCamel #2 (r + 3)km/hr 4 hr 4(r+3)

4 4 3 68r r

3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first?

Rate Time Distance1st Plane2nd Plane

3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first?

Rate Time Distance1st Plane 270 mph2nd Plane 450 mph

3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first?

Rate Time Distance1st Plane 270 mph t2nd Plane 450 mph t – 2

3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first?

Rate Time Distance1st Plane 270 mph t 270t2nd Plane 450 mph t – 2 450(t – 2)

270 450 2t t

4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles.

Rate Time DistanceEastboundWestbound

4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles.

Rate Time DistanceEastbound 420 mphWestbound 350 mph

4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles.

Rate Time DistanceEastbound 420 mph tWestbound 350 mph t – 2

4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles.

Rate Time DistanceEastbound 420 mph t 420tWestbound 350 mph t – 2 350(t – 2)

420 450 2 3535t t

Thursday Homework

Study for uniform motion quiz by doing practice problems