Answer:
56 hours 25 minutes
Step-by-step explanation:
Given:
Suppose it takes 45 hours for robot A to construct a new robot
It takes 25 hours for both robots to construct a new robot.
Question asked:
How long would it take robot B to construct a new robot, working alone ?
Solution:
Let the time taken by robot B to construct new robot = ![x](https://tex.z-dn.net/?f=x)
<u>By robot A</u>
It takes 45 hours to construct = 1 new robot
It takes 1 hour to construct = ![\frac{1}{45} \ new\ robot](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B45%7D%20%5C%20new%5C%20robot)
<u>By robot B</u>
It takes
hours to construct = 1 new robot
It takes 1 hour to construct =
new robot
<u>By working together</u>
It takes 25 hours to construct = 1 new robot
It takes 1 hour to construct = ![\frac{1}{25} \ new\ robot](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B25%7D%20%5C%20new%5C%20robot)
new robot is constructed in = 1 hour
<u><em>New robot is constructed by both working together in 1 hour = New robot is constructed by robot A in 1 hour + New robot is constructed by robot B in 1 hour </em></u>
![\frac{1}{25} =\frac{1}{45} +\frac{1}{x} \\](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B25%7D%20%3D%5Cfrac%7B1%7D%7B45%7D%20%2B%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C)
Subtracting both sides by ![\frac{1}{45}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B45%7D)
![\frac{1}{25}-\frac{1}{45} =\frac{1}{45} -\frac{1}{45}+\frac{1}{x} \\\\\frac{1}{25}-\frac{1}{45} =\frac{1}{x}\\\\ Taking\ LCM \ of \ 25\ and\ 45,\ we\ got\ 225](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B25%7D-%5Cfrac%7B1%7D%7B45%7D%20%3D%5Cfrac%7B1%7D%7B45%7D%20-%5Cfrac%7B1%7D%7B45%7D%2B%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7B25%7D-%5Cfrac%7B1%7D%7B45%7D%20%3D%5Cfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%20Taking%5C%20LCM%20%5C%20of%20%5C%2025%5C%20and%5C%2045%2C%5C%20we%5C%20got%5C%20225)
![\frac{9-5}{225} =\frac{1}{x} \\ \\ \frac{4}{225} =\frac{1}{x}\\\\ By\ cross \ multiplication\\4\times x=225\\Dividing\ both\ sides\ by\ 4\\x=56.25\ hours](https://tex.z-dn.net/?f=%5Cfrac%7B9-5%7D%7B225%7D%20%3D%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C%20%5C%5C%20%5Cfrac%7B4%7D%7B225%7D%20%3D%5Cfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%20By%5C%20cross%20%5C%20multiplication%5C%5C4%5Ctimes%20x%3D225%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%204%5C%5Cx%3D56.25%5C%20hours)
Thus, robot B would take 56 hours 25 minutes to construct a new robot, working alone.