Question

p take 5 hours more than q to complete a work.working together they completed the work in 6 hours,q alone could complete the work in

Answer 1

p = 15 hours

and

q = 10 hours

Answer 2

$\text{Let the work complete by Q by x hours.}$

$\text{So, P takes x + 5 hours to complete the work.}$

Now,

= > $\large{ \frac{1}{x} + \frac{1}{x + 5} = \frac{1}{6} }$

= > $\large{ \frac{x \: + \: 5 \: + \: x}{x(x + 5)} = \frac{1}{6} }$

= > $(2x + 5)6 = {x}^{2} + 5x$

= > ${x}^{2} + 5x = 12x + 30$

= > ${x}^{2} - 7x - 30 = 0$

= > ${x}^{2} - 10x + 3x - 30 = 0$

= > $x(x - 10) + 3(x - 10) = 0$

= > $(x + 3)(x - 10) = 0$

= > $x = 10$

Therefore, $\bold{\fbox{Q = 10 \:hours}}$