If Alex takes 6 hours to paint a wall, but it takes 4 hours for David to paint the same wall, how long does it take to paint that wall if th

Here's an easy way to work this kind of problem......

Alex paints 1/6 of the wall in one hour and David paints 1/4 of the wall in one hour.

Let's just add these fractions...

1/6 + 1/4  = 10/24

Now...just take the reciprocal of this

24/10 = 2.4    .....and there's your answer (in hours)

An appropriate equation is:

     rate x time (of the first person) +  rate x time (of the second person)  =   amount completed

Alex's rate is 1 wall painted in 6 hours, which is:  1 wall / 6 hrs

David's rate is 1 wall painted in 4 hours, which is:  1 wall / 4 hrs

Amount completed is 1 wall.

The time is the same for both, so let's use the variable  t.

    (1/6)·(t)  +  (1/4)·(t)   =   1

         t / 6   +   t / 4        =   1

Simplify the equation by multiplying both sides by a common denominator; I'll use 24:

     (24) · (1/6)·(t)  +  (24) · (1/4)·(t)    =  (24) · 1

            4t   +   6t   =  24

                      10t   =   24

                          t   =   2.4 hours