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wolverine [178]
3 years ago
14

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
Mathematics
2 answers:
puteri [66]3 years ago
7 0

Answer:

56 hours 25 minutes

Step-by-step explanation:

Len [333]3 years ago
4 0

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

<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

<u>By robot B</u>

It takes x hours to construct = 1 new robot

It takes 1 hour to construct = \frac{1}{x} 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

\frac{1}{25} 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} \\

Subtracting both sides by \frac{1}{45}

\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

\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

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

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