Question

A takes x hours to complete a task. B takes 5 more hours than A. If they work together, they can complete the task in 6 hours. Find the value of x.​

Answer 1

Let A alone take X hours

Then X takes (X+5) hours

Together in 1 hour they finish 1/X + 1/(X+5) of the work

Since together they take 6 hours, in 1 hour they finish 1/6 of the work

$\qquad \longrightarrow\sf \: \frac{1}{x }+ \frac{1}{(x+5)} = \frac{1}{6}$

$\qquad \longrightarrow \sf \: 6(x+5) +6x = x^2 + 5x \\ \\ \qquad \longrightarrow \sf \: x^2 -7x -30 = 0$

• (X-10) ( X+3) =0

• X = 10 hours

ANSWER A alone takes 10 hours and B takes 15 hours