Question

It takes 6 workers from the Fast Movers Company 10 hours to unload 6 trucks. It takes 10 workers from the Careful Movers Company 8 hours to load 2 trucks. How long would it take 4 workers from the Fast Movers Company and 8 workers from the Careful Movers Company to unload 8 trucks?

Answer 1

The time it would take 4 workers from the Fast Movers Company and 8 workers from the Careful Movers company to unload 8 trucks is 13 hours and 20 minutes

Explanation:

The time it takes 6 workers from the Fast Movers Company to unload 6 trucks = 10 hours

The time it takes 10 workers from the Careful Movers Company to load 2 trucks = 8 hours

Therefore, when 1 worker of the Fast Movers Company is unload 1 truck each of the 6 trucks it takes 10 hours

Which gives the time for 1 worker of the Fast Movers Company is unload 1 truck = 10 hours, which gives;

10 worker hours per truck or 10 worker·h/(truck)

Similarly we have;

The time it takes 10 workers of the Careful Movers Company to load 2/2 = 1 truck = 8/2 = 4 hours

Therefore, the time it would take 1 worker of the Careful Movers Company to load 1 truck = 10 × 4 hours = 40 hours, which gives;

40 worker·h/(truck)

Let "t" represent the time it would take 4 workers from the Fast Movers Company and 8 workers from the Careful Movers Company to unload 8 trucks

We have;

`(4 \ workers * t )/(\left ((10 \ worker \cdot hour)/(truck) \right ) ) + (8 \ workers * t )/(\left ((40 \ worker \cdot hour)/(truck) \right ) ) = 8 \ trucks`

Which can be simplified as follows;

`(4 \ trucks * t )/(10 \cdot hour) + (8 \ trucks * t )/(40 \cdot hour) = t * \left ( (4 \ trucks )/(10 \cdot hour) + (8 \ trucks )/(40 \cdot hour) \right ) = 8 \ trucks`

`t = (8 \ trucks)/(\left ( (4 \ trucks )/(10 \cdot hour) + (8 \ trucks )/(40 \cdot hour) \right ) ) = (8 \ trucks)/(\left ( (3 \ trucks )/(5 \ hour) \right ) ) = (5 \ hour* 8 \ trucks)/(3 \ trucks ) \right ) } = (40)/(3) \ hours`

t = 40/3 hours = 13 hours and 20 minutes

The time it would take 4 workers from the Fast Movers Company and 8 workers from the Careful Movers company to unload 8 trucks = 13 hours and 20 minutes