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 = [tex]x[/tex]
By robot A
It takes 45 hours to construct = 1 new robot
It takes 1 hour to construct = [tex]\frac{1}{45} \ new\ robot[/tex]
By robot B
It takes [tex]x[/tex] hours to construct = 1 new robot
It takes 1 hour to construct = [tex]\frac{1}{x}[/tex] new robot
By working together
It takes 25 hours to construct = 1 new robot
It takes 1 hour to construct = [tex]\frac{1}{25} \ new\ robot[/tex]
[tex]\frac{1}{25}[/tex] new robot is constructed in = 1 hour
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
[tex]\frac{1}{25} =\frac{1}{45} +\frac{1}{x} \\[/tex]
Subtracting both sides by [tex]\frac{1}{45}[/tex]
[tex]\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[/tex]
[tex]\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[/tex]
Thus, robot B would take 56 hours 25 minutes to construct a new robot, working alone.
