Question

Suppose it takes 45 hours for robot A to construct a new robot. Working together with robot B, it takes 25 hours for both robots to construct a new robot. How long would it take robot B to construct a new robot, working alone

Answer 1

45?

Explanation:

Answer 2

56 hours 25 minutes

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`

By robot A

It takes 45 hours to construct = 1 new robot

It takes 1 hour to construct =
`(1)/(45) \ new\ robot`

By robot B

It takes
`x` hours to construct = 1 new robot

It takes 1 hour to construct =
`(1)/(x)` new robot

By working together

It takes 25 hours to construct = 1 new robot

It takes 1 hour to construct =
`(1)/(25) \ new\ robot`

`(1)/(25)` 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

`(1)/(25) =(1)/(45) +(1)/(x) \\`

Subtracting both sides by
`(1)/(45)`

`(1)/(25)-(1)/(45) =(1)/(45) -(1)/(45)+(1)/(x) \\\\(1)/(25)-(1)/(45) =(1)/(x)\\\\ Taking\ LCM \ of \ 25\ and\ 45,\ we\ got\ 225`

`(9-5)/(225) =(1)/(x) \\ \\ (4)/(225) =(1)/(x)\\\\ By\ cross \ multiplication\\4* x=225\\Dividing\ both\ sides\ by\ 4\\x=56.25\ hours`

Thus, robot B would take 56 hours 25 minutes to construct a new robot, working alone.