As it says in the question： if one person can do a job in 4 hours, and another can do the job in 3 hours, how quickly can they do the job together in they can work together?
My attempt was this: Average them together, $\frac{3+4}{2}=3.5$, then say that these workers take an average of 3.5 hours to do the job, together, they should be able to do it half of their average time, $\frac{7}{4}$ hours, which is one hour 45 minutes.
The answer is apparently 1 hour and 15 minutes. Where did I go wrong?
A's power is $P_A=\frac{W_A}{t_A}$, where $W_A$ is the "work" produced by A in time $t_A$. So, if A finishes $1$ piece of work in $4$ hours, then his power is $$P_A=\frac{1}{4}$$ B's power is $P_B=\frac{W_B}{t_B}=\frac{1}{3}$. When A and B work simultaneously their powers add to produce the total power: $$P_{AB}=P_{A}+P_{B}\Leftrightarrow\frac{W_{AB}}{t_{AB}}=\frac{W_A}{t_A}+\frac{W_B}{t_B}\Leftrightarrow\frac{1}{t_{AB}}=\frac{1}{4}+\frac{1}{3}$$ Now you just have to solve the last equation for $t_{AB}$.