10.7 Using Rational Equations

• Goal: To solve problems involving work questions using RE

Everett can bike 10 miles per hour. Lavern can bike 15 miles per hour. Austin and Beaumont are 250 miles apart. In how many hours will they meet if they leave at the same time?

250E Ld d 10 15 250t t

25 250t 10 t hours

Ld r t Ed r t 10 15A B

Everett could make the entire distance by himself in ______ hours.

1

25trip

hours

rate

25

Everett can bike from Vinton to Beaumont in 5 hours. It takes Lavern 4 hours. . In how many hours will they meet if they leave at the same time?

1E L tripd d

4 5 20t t 20

9

t hours

Ld r t Ed r tV B

1

4trip

hours

1

5trip

hours

15 4

t t 20(

)1 1

15 4t t

Everett can bike Ville Platt to Guedon in 10 hours. Lavern can bike the same trip in 15 hours. If how many hours will they meet if they leave at the same time?

1E Ld d

110 15

t t

3 2 30t t

6 t hours

Ed r t 1

10

30( )

Ld r t 1

15

Everett can bike from CutnShoot to Beaumont in 5 hours. It takes Lavern 6 hours. . In how many hours will they meet if they leave at the same time?

1E L tripd d 6 5 30t t

2.7 t hours

Ld r t Ed r tC B

1

6trip

hours

1

5trip

hours

30( )

15 6

t t

30

11t

2 hours and 42 minutest

Everett can type a term paper in 8 hours. Laverne can type the same term paper in 12 hours. How long will it take them to type it if they work together? Ed r t Ld r t1

8

1

12

1E Ld d

1 11

8 12t t

3 2 24t t 5 24t

4.8t hours24( )

Helen can paint a living room in 5 hours. If Bill helps Helen they can paint the room in 3 hours. How long would it take Bill to paint the living room alone?Let x =# hours it will

take Bill Hd r t Bd r t

1H Bd d

1

5

1

x

3

51

3

x

3 3

5x

7.5hours5x( )

3x 1515 2x

Al can paint a living room in 3 hours. If Henry helps Al they can paint the room in 2 hours. How long would it take Henry to paint the living room alone?Let x =# hours it will

take H Ad r t Hd r t

1H Bd d

1

3

1

x

2

31

2

x

2 1

3x

6 hoursx

Virginia can deliver the papers on her paper route in 30 minutes. When her brother Wayne takes the route, it takes him 40 minutes. How long does it take if they deliver the papers together?

min7

117t

Vd r t Wd r t

1V Wd d

1

30

1

40

430 0

t t 120

7t

4(10)

3(10)

120( )

4 3 120t t

Virginia can deliver the papers on her paper route in 20 minutes. When her brother Wayne takes the route, it takes him 30 minutes. How long does it take if they deliver the papers together?

12mint

Vd r t Wd r t

1V Wd d

1

20

1

30

320 0

t t 60

5t 60( )

3 2 60t t

The reciprocal of 7 and the reciprocal of 3 is the same as the reciprocal of what number?

1 1 1

7 3 x

3 7 21x x 21

10x

:

1 1 10?

7 3 21

check

21x( )

The additive inverse of a number divided by 16 is the same as one less than three times its reciprocal. Find the number.

13 1

16

x

x

4 or 12x

31

16

x

x

3

16

x x

x

2 16 3x x 20 16 48x x

x

x 0 4 12x x

The reciprocal of 2 more than a number is three times the reciprocal of the number. Find the number. 1 1

32x x

1 3 2x x

3x

:

1 13 ?

3 2 3

check

1 3

2x x

1 3 6x x 6 2x

Page 458, #6

d r t

d r t

120

120 2r -3

2 3r t r t

r r 2 3t t

2 6t t 6t

120 t r 6

20 r

Page 458, (6 and 8 – 10)

1 1 1

4 5 x

20

9

1 51

2

x

x x

10 or -10

Page 458, (6 and 8 – 10)

31

12

x

x

6

12 3

12 12

x

x

12 3

12

x

x

212 36x x

20 12 36x x

0 6 6x x

Assignment:Page 458

#’s(2-16) even (21-24) allWrite the questions down