Question

Direct and Inverse variation: The number of hours needed to assemble computers varies directly as the number of computers and inversely as the number of workers. If 4 workers can assemble 12 computers in 9 hours, how many workers are needed to assemble 48 computers in 8 hours?

Answer 1

Hint: In this problem, we have to find the number of workers needed to assemble 48 computers in 8 hours, if 4 workers can assemble 12 computers in 9 hours. Since, The number of hours needed to assemble computers varies directly as the number of computers and inversely as the number of workers, we can find the answer.

Complete step-by-step answer:
We know that 4 workers can assemble 12 computers in 9 hours.
We also know that, since the number of hours is directly proportional to the number of computers.
\[\Rightarrow 4\times 12=48\]
48 computers can be assembled by 4 workers in,
\[4\times 9=36\] hours.
 We also know that, since the number of hours is inversely proportional to the number of workers.
48 computers could be assembled by,
\[\dfrac{9}{2}\times 4=18\]
48 computers could be assembled by 18 workers in,
\[\dfrac{2}{9}\times 36=8\] hours.
Therefore, 48 computers could be assembled by 18 workers in 8 hours.

Note: Students make mistakes while going through the given data, as the number of hours needed to assemble computers varies directly as the number of computers and inversely as the number of workers. We should also concentrate while multiplying the correct number as per the variations.