Question

Two people working together can finish the work in $\frac{22}{55}$ minutes. If one person takes 8 minutes more than the other person to finish it, find the second degree equation from which we can find time in which the faster person would finish the work.

• A. $45x^2+396x-176=0$
• B. $55x^2+396x-176=0$
• C. $55x^2+386x-176=0$
• D. $55x^2+396x-186=0$

Answer 1

The correct option is B

$55x^2+396x-176=0$

Let the faster person take $x$ minutes to finish the work. Therefore, the slower person will take $(x+8)$ minutes to finish the work.

$\therefore$ The part of the work finished by the faster person in one minute $=\frac{1}{x}$

$\Rightarrow$ The part of the work finished by the slower person in one minute $=\frac{1}{x+8}$

It is given that the work is finished in $\frac{22}{55}$ minutes

$\Rightarrow$The part of the work finished in one minute by both the people together $=\frac{55}{22}$

$\Rightarrow \frac{1}{x}+\frac{1}{x+8}=\frac{55}{22}$

$\frac{x+8+x}{x(x+8)}=\frac{55}{22}$

$\Rightarrow 22(2x+8)=55x(x+8)$

$\Rightarrow 44x+176=55x^2+440x$

$\Rightarrow 55x^2+396x-176=0$