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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

User Chuck Vose
by
8.0k points

2 Answers

7 votes

Answer:

45?

Explanation:

User Nonso
by
8.3k points
3 votes

Answer:

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.

User Ironv
by
8.1k points
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