Respuesta :
Answer:
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
Step-by-step 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;
[tex]\dfrac{4 \ workers \times t }{\left (\dfrac{10 \ worker \cdot hour}{truck} \right ) } + \dfrac{8 \ workers \times t }{\left (\dfrac{40 \ worker \cdot hour}{truck} \right ) } = 8 \ trucks[/tex]
Which can be simplified as follows;
[tex]\dfrac{4 \ trucks \times t }{10 \cdot hour} + \dfrac{8 \ trucks \times t }{40 \cdot hour} = t \times \left ( \dfrac{4 \ trucks }{10 \cdot hour} + \dfrac{8 \ trucks }{40 \cdot hour} \right ) = 8 \ trucks[/tex]
[tex]t = \dfrac{8 \ trucks}{\left ( \dfrac{4 \ trucks }{10 \cdot hour} + \dfrac{8 \ trucks }{40 \cdot hour} \right ) } = \dfrac{8 \ trucks}{\left ( \dfrac{3 \ trucks }{5 \ hour} \right ) } = \dfrac{5 \ hour\times 8 \ trucks}{3 \ trucks } \right ) } = \dfrac{40}{3} \ hours[/tex]
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
