If one student can complete the decorations for the prom in 5 days working alone, another student could do it in 3 days, and a third could do it in 4 days, how long would it take them working together?

Question

michele_laino · Answer

If I call with $D$ the decoration, then the working rates of the three students, are:
$$\Large \frac{D}{5},\;\frac{D}{3},\;\frac{D}{4}$$
respectively.
So, if they work together, then after $t$ hours, the work $D$ is completed, and $t$ is such that:
$$\Large  t\left( {\frac{D}{5} + \frac{D}{3} + \frac{D}{4}} \right) = D$$
please solve that equation for $t$

michele_laino · Answer

oops.. $t$ is the number of days

joshoyen · Answer

ohhh okay thanks!