Three machines perform together a certain job. If only machine A works, to perform the job alone, it would require a hours more than the time required to perform the job by the 3 machines, when they work together. If only machine B works, to perform the job alone, it would require b hours more than the time required to perform the job by the 3 machines, when they work together. If only machine C works, to perform the job alone, it would require c times more hours more than the time required to perform the job by the 3 machines, when they work together. In how much time each of the machines would complete the work, if it were to work by itself? The solution must be expressed using a,b,c .
How do I even begin this?
Let $D$ be the number of hours machine A would take to do the job. Similarly $E$ for machine B and $F$ for machine $C$. That means in one hour A can do $\frac 1D$ of the job. How much can the three machines do together in one hour? If you take the reciprocal of that, you have the number of hours the three machines take to do the job together, we will call it $H$. Now write the three equations based on the text: $D=a+H$ You are looking to express $D,E,F$ as an expression involving $a,b,c$