Math Question

[HowAboutDAT]

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Machines A and B always operate independently at their respective constant rates. When working alone, machine A can fill a production lot in 5 hours, and machine B can fill a separate production lot of the same size in x hours. When the two machines operate simultaneously to fill both production lots, it takes them 4 hours to complete the job. What is the value of x?

and


If it takes machine A 2 hours to do seven jobs, machine B 5 hours to do three jobs, and then ask how long it would take them to do 12 jobs working simultaneously?

thanks guys

 

[GiTsticker]

For the first one, you have two independent speeds, and one combined speed. The formula to express this is (Time 1 x Time 2) / (Time 1 + Time 2) = Combined time. Time one is 5, time 2 is x, total time is 4.

5x / (5 + x) = 4
5x = 20 + 4x
x = 20

 

[UCB05]

Machines A and B always operate independently at their respective constant rates. When working alone, machine A can fill a production lot in 5 hours, and machine B can fill a separate production lot of the same size in x hours. When the two machines operate simultaneously to fill both production lots, it takes them 4 hours to complete the job. What is the value of x?

and


If it takes machine A 2 hours to do seven jobs, machine B 5 hours to do three jobs, and then ask how long it would take them to do 12 jobs working simultaneously?

thanks guys

A does 7/2 jobs per hour. B does 3/5 jobs per hour. Together, they do 7/2 + 3/5 = 4.1 jobs per hour. 12 jobs/ 4.1 jobs per hour= 2.93 or round up to 3 hours. Fraction wise: 12/ (41/10)=120/41 or approx 3 hours

 

[GiTsticker]

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