In three hours, Company ABC can make X ball bearings. Company DEF can make X ball bearings in 4 hours. Company GHI can make X ba
1 answer:
Answer:
<em>X ball bearings will be made in 1 hour and 20 minutes</em>
Step-by-step explanation:
<u>Proportions </u>
The proportions give us an important tool to easily solve common problems of any type. We know that:
Company ABC can make X ball bearings in 3 hours.
Company DEF can make X ball bearings in 4 hours.
Company GHI can make X ball bearings in 6 hours.
In one hour, each company can make
ABC: X/3 ball bearings
DEF: X/4 ball bearings
GHI: X/6 ball bearings
Working together, they can make
ball bearings. Operating
If they can make 3/4 of a ball bearing in one hour, then one complete ball bearing will need
hours to complete. It's equivalent to 1 1/3 hours or 1 hour and 20 minutes
X ball bearings will be made in 1 hour and 20 minutes
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Check the picture below.
![\bf A=\cfrac{h(a+b)}{2}\quad \begin{cases} A=20\\ a=6z-1\\ b=2z+3\\ h=z \end{cases}\implies 20=\cfrac{z[(6z-1)~+~(2z+3)]}{2} \\\\\\ 20=\cfrac{z(8z+2)}{2}\implies 20=\cfrac{2z(4z+1)}{2}\implies 20=z(4z+1) \\\\\\ 20=4z^2+z\implies 0=4z^2+z-20](https://tex.z-dn.net/?f=%5Cbf%20A%3D%5Ccfrac%7Bh%28a%2Bb%29%7D%7B2%7D%5Cquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D20%5C%5C%0Aa%3D6z-1%5C%5C%0Ab%3D2z%2B3%5C%5C%0Ah%3Dz%0A%5Cend%7Bcases%7D%5Cimplies%2020%3D%5Ccfrac%7Bz%5B%286z-1%29~%2B~%282z%2B3%29%5D%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0A20%3D%5Ccfrac%7Bz%288z%2B2%29%7D%7B2%7D%5Cimplies%2020%3D%5Ccfrac%7B2z%284z%2B1%29%7D%7B2%7D%5Cimplies%2020%3Dz%284z%2B1%29%0A%5C%5C%5C%5C%5C%5C%0A20%3D4z%5E2%2Bz%5Cimplies%200%3D4z%5E2%2Bz-20)
since the height is just a length unit, it can't be -2.3646.
since the height is just a length unit, it can't be -2.3646.