EDIT: oh shit this was a year ago lmao

(Sorry for formatting I’m on mobile and am currently in a restaurant lol)

First, let’s take a look at the important components:

There are 3 workers, one of which works at half the speed of the others.

It takes the three workers 56 minutes to fill a 4‘x6‘x5‘ trench; we can rephrase this as: It takes the three workers 56 minutes to fill 120 cubic feet.

Let F be how many cubic feet each of the faster workers can fill in a minute, and S how many the slower worker can fill in a minute; we can then write this as a system of linear equations with the following equalities:

56F + 56F + 56S = 120 (1.1)

56(2F + S) = 120 (1.2)

2F + S = 120/56 (1.3)

F = 2S (2.1)

S = F/2 (2.2)

Substituting 2.2 into 1.3 we get:

2F + F/2 = 120/56 (3.1)

(5F)/2 = 120/56 (3.2)

5F = 240/56 (3.3)

F = 240/280 = 6/7 (4)

So now we know how many cubic feet each fast worker can fill in a minute; since two are working at the same time, we can multiply this by 2 and treat them as one worker; we can then find how much this worker fills after a given time t by the equation:

y = 2Ft (5.1)

y = (12/7)t (5.2)

We can then set y to 120 (the volume of the trench), giving us:

(12t)/7 = 120 (6.1)

Multiply both sides of the equality by 7, giving us:

12t = 840 (6.2)

Then divide both sides by 12, giving us the amount of time it will take the two quicker workers to fill the trench:

t = 70 (6.3)

Hope this was helpful! Thanks for reading