It takes an apprentice four times as long as the experienced plumber to replace the pipes under an old house. If it takes them 9 hours when they work together, how long would it take the apprentice alone?

It takes an apprentice four times as long as the experienced plumber to replace the pipes under an old house. It takes them 14 hours when they work together.

Step-by-step explanation:

5/(4x) = 1/14

x = 35/2

The plumber takes x = 35/2 hours to replace the pipes alone.

The apprentice takes 4x = 70 hours to replace the pipes alone.

a 10 percent increase

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}