Processor Word Problem

Question

It takes 12 processor 5 min to calculate 6 solutions. If 40 processor are in two groups, where grou 1 has 4 more processors than the 2nd group, how long will it take the 2nd group to calculate 27 solutions

Answer 1

If $12$ processors can compute $6$ solutions in $5$ minutes, then $2$ processors can compute $1$ solution in $5$ minutes, and so $1$ processor can compute $1$ solution in $10$ minutes. Now, we need to find the number of processors in the two groups, say $p_f$ and $p_s$ for the first and second groups, respectively. We have that $p_f+p_s=40$ and $p_f-p_s=4$. Solving for the two variables, we get that $p_f=22$ and $p_s=18$. That means that the second group, the group that we will work with for this problem, has $18$ processors. If $1$ processor can compute $1$ solution in $10$ minutes, then $18$ processors can compute $18$ solutions in $10$ minutes. We need $27$ solutions, not $18$, so we multiply the time spent computing by $\frac{27}{18}=\frac{3}{2}$ to give $10\cdot\frac{3}{2}=15$. Thus, the second group of processors can compute $27$ solutions in $\boxed{15}$ minutes.