Respuesta :
Answer:
The faster computer can do the job in 20 mins on it own.
Step-by-step explanation:
Given:
Time taken by slower computer to do job on its own =30 minutes.
Time taken by both the computers to do the job = 12 mins.
We need to find the Time taken by faster computer to do job on its own.
Solution:
Let the the Time taken by faster computer to do job on its own be 'x'.
Now we know that;
Rate to complete the job is equal to number of jobs divided by time taken to complete the job.
Rate of faster computer = [tex]\frac1x[/tex]
Rate of slower computer = [tex]\frac{1}{30}[/tex]
Rate of both the computers = [tex]\frac{1}{12}[/tex]
Now we can say that;
Rate of both the computers is equal to sum of Rate of faster computer and Rate of slower computer.
framing in equation form we get;
[tex]\frac{1}{12}=\frac{1}{30}+\frac{1}{x}\\\\\frac{1}{x} = \frac{1}{12}-\frac{1}{30}[/tex]
Now we will take the LCM to make the denominator common we get;
[tex]\frac{1}{x}=\frac{5}{12\times5}-\frac{2}{30\times2}\\\\\frac1x=\frac{5}{60}-\frac{2}{60}[/tex]
Now denominator are same so we will solve the numerator.
[tex]\frac1x=\frac{5-2}{60}\\\\\frac1x=\frac{3}{60}\\\\\frac1x=\frac{1}{20}\\\\x=20\ mins[/tex]
Hence The faster computer can do the job in 20 mins on it own.
