Question

A would have taken 12 hours less than what B would have taken to completed a task if both of them worked alone. Working together they can complete a task in 17.5 hours. How many hours would B take to do the 50% of the task?

Answer 1

Step-by-step explanation:

let b be x hrs

a=x-12 hrs

when they work together:-

b+a=(x+x-12) hrs

working together they

complete task in=17.5hrs

atq,2x-12=17.5

2x=17.5+12

2x=29.5

x=29.5/2

x=14.75

a=14.75-12= 2.75

b did =(14.75+2.75)/1/2

=8.75

b's work done =8.75

Answer 2

Let B takes time to complete a task=x hours

A takes time to complete a task=x-12 hours

If they worked together , time taken to complete a task =17.5 hours

To find:

Time required for B to do complete  the 50% of the task.

B complete task in 1 hr=$\frac{1}{x}$

A complete task in hr=$\frac{1}{x-12}$

According to question

$\frac{1}{x}+\frac{1}{x-12}=\frac{1}{17.5}$

$\frac{x-12+x}{x(x-12)}=\frac{10}{175}$

$\frac{2x-12}{x(x-12)}=\frac{2}{35}$

$35(2x-12)=2x(x-12)$

$70x-420=2x^2-24x$

$2x^2-24x-70x+420=0$

$2x^2-94x+420=0$

$x^2-47x+210=0$

$x=\frac{47\pm\sqrt{(47)^2-4\times 210}}{2}$

Using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{47\pm 37}{2}$

$x=\frac{47+37}{2}=42$

$x=\frac{47-37}{2}=5$ is not possible

Because 5-12=-7

Time cannot be negative

B takes time to complete a task=42 hours

B takes time to complete 50% of the task=$\frac{50}{100}\times 42=21hours$