UNIFORM MOTION PROBLEMS

Jo & Jim are 240 miles apart. Jo starts Jo & Jim are 240 miles apart. Jo starts toward Jim at 55 mph at the same time Jim toward Jim at 55 mph at the same time Jim starts toward Jo at 65 mph. How long until starts toward Jo at 65 mph. How long until

they meet?they meet?

Jo

Jim

r t d

d = rt

UNIFORM MOTION PROBLEMS

Jo & Jim are 240 miles apart. Jo starts Jo & Jim are 240 miles apart. Jo starts toward Jim at 55 mph at the same time Jim toward Jim at 55 mph at the same time Jim starts toward Jo at 65 mph. How long until starts toward Jo at 65 mph. How long until

they meet?they meet?

Jo

Jim

r t d

55

65

t

t

55t

65t

55t + 65t = 240 SOLVE

UNIFORM MOTION PROBLEMS

Rob & Rae leave the same place at the same time Rob & Rae leave the same place at the same time going in different directions. If Rob is traveling going in different directions. If Rob is traveling at 28 mph and Rae is traveling at 19 mph, how at 28 mph and Rae is traveling at 19 mph, how

long until they are 150 miles apart?long until they are 150 miles apart?

Rob

Rae

r t d

28

19

t

t

28t

19t

28t + 19t = 150 SOLVE

UNIFORM MOTION PROBLEMS

Tim heads west at 50 mph. Tom leaves 1 hour Tim heads west at 50 mph. Tom leaves 1 hour later (heading west) at 60 mph. How long until later (heading west) at 60 mph. How long until

Tom catches Tim?Tom catches Tim?

Tim

Tom

r t d

50

60

t + 1

t

50(t + 1)

60t

50(t + 1) = 60t SOLVE

MIXTURE PROBLEMS

How much 12% nitrogen should you mix with How much 12% nitrogen should you mix with 20% nitrogen to get 100 lbs. of 17% nitrogen?20% nitrogen to get 100 lbs. of 17% nitrogen?

+ =

x 100 - x 100

12% 20% 17%

.12x

SOLVE

+ .20(100 – x) = .17(100)

MIXTURE PROBLEMS

How much 30% acid should you mix with 5 pints How much 30% acid should you mix with 5 pints of 55% acid to get 25% acid?of 55% acid to get 25% acid?

+ =

x 5 x + 5

30% 55% 25%

.30x

SOLVE

+ .55(5) = .25(x + 5)

SAMPLE PROBLEM

How much pure antifreeze should you mix with 6 How much pure antifreeze should you mix with 6 quarts of 45% antifreeze to get 60% antifreeze?quarts of 45% antifreeze to get 60% antifreeze?

+ =

x 6 x + 6

100% 45% 60%

1x

SOLVE

+ .45(6) = .60(x + 6)

SAMPLE PROBLEM

How much pure antifreeze should you mix with 6 How much pure antifreeze should you mix with 6 quarts of 45% antifreeze to get 60% antifreeze?quarts of 45% antifreeze to get 60% antifreeze?

+ =

x 6 x + 6

100% 45% 60%

1x

SOLVE

+ .45(6) = .60(x + 6)

Rene and Ronnie are 240 miles apart. If they Rene and Ronnie are 240 miles apart. If they start out toward each other at the same time, start out toward each other at the same time,

how long will it take them to meet if Rene travels how long will it take them to meet if Rene travels at 40 mph and Ronnie travels at 60 mph.at 40 mph and Ronnie travels at 60 mph.

Rene

Ronnie

r t d

40

60

t

t

40t

60t

40t + 60t = 240 SOLVE

SAMPLE PROBLEM

PROBLEM #8

The Nut Shoppe sells walnuts for $4 a pound and The Nut Shoppe sells walnuts for $4 a pound and cashews for $7 a pound. How many pounds of cashews cashews for $7 a pound. How many pounds of cashews should be mixed with 10 pounds of walnuts to obtain a should be mixed with 10 pounds of walnuts to obtain a

mixture that sells for $5.50 a pound?mixture that sells for $5.50 a pound?

+ =

10 x x + 10

$4 $7 $5.50

4(10) + 7x = 5.50(x + 10)

PROBLEM #10

Two cyclists begin traveling in the same direction Two cyclists begin traveling in the same direction on the same bike path, leaving at the same time. on the same bike path, leaving at the same time.

One travels at 20 mph, and the other travels at 14 One travels at 20 mph, and the other travels at 14 mph. When will they cyclists be 15 miles apart?mph. When will they cyclists be 15 miles apart?

Cyclist A

Cyclist B

r t d

20

14

t

t

20t

14t

20t – 14t = 15

PROBLEM #22

Madison HS band sold gift wrap. The wrap in solid Madison HS band sold gift wrap. The wrap in solid colors sold for $4 per roll, and the print wrap sold for colors sold for $4 per roll, and the print wrap sold for $6 per roll. They sold 480 rolls and collected $2340. $6 per roll. They sold 480 rolls and collected $2340.

How many rolls of each kind were sold?How many rolls of each kind were sold?

+ =

x 480 - x

$4 $6 $2340

4x + 6(480 – x) = 2340

THE FIRST STUDENT TO EMAILTHE FOLLOWING SENTENCES TO ME

WILL RECEIVE 5 BONUS POINTS:

“This message is to let you know that I have gone through the PowerPoint on mixture problems and am

claiming the 5 bonus points promised to the first student to submit this email.”