Question

A can do a piece of work in 3 days less than



b. A and b can do together in 15 days. How many can a alone do?

Answer 1

Answer:

$\frac{33+\sqrt{909}}{2}-3$

Step-by-step explanation:

1.) Let x be the number of days that B can do the work alone and x-3 be the number of days that A can do the work alone.

2.) We have $\frac{1}{x-3},\frac{1}{x}$ as the work rates (work done per day) of A and B, respectively.

3.) Together they can do the entire work in 15 days

$\frac{1}{x-3}+\frac{1}{x}=\frac{1}{15}$

4.) Solving for x, we get

$(15x(x-3))(\frac{1}{x-3}+\frac{1}{x})=(\frac{1}{15})(15x(x-3))$

$15x+15(x-3)=x(x-3)$

$15x+15x-45=x^2-3x$

$0=x^2-33x+45$

5.) Using quadratic formula,

$x=\frac{33+\sqrt{909}}{2}$

6.) A can do a piece of work in $\frac{33+\sqrt{909}}{2}-3$ days

Answer 2

Answer:

A can do a piece of work in 3 days less than b. A and b can do together in 15 days.  Then A alone can do in 28.575 days

Step-by-step explanation:

Let Say B take   number of days to work = B   Days

A take number of days to work  = B - 3   Days

B's 1 day work  = 1/B

A's 1 Day work = 1/(B-3)

A's & B's together 1 day work =  1/B + 1/B-3

= (2B-3)/(B(B-3))

A& B together will complete work in    B(B-3)/(2B-3)

B(B-3)/(2B-3) = 15

=> B² - 3B = 30B - 45

=> B² - 33B + 45 = 0

B = (33 ± √(-33² - 4(45)) )/2

=> B = (33 ±  30.15)/2

=> B = 31.575     B = 1.425

A = B -3

A = 28.575 Days     or A = -1.57 (-ve is not possoble)

so A alone will complete in 28.575 days