14.Workdays. Three workers are digging a pit. They work in turns, and each works as long as the other two need to dig half the pit. Working this way, they dug the pit. How many times faster would they have finished the work if they had worked simultaneously

## 43 Languages of Mathematics
14. Let each of them work for $a, b$, and $c$ hours respectively. Consequently, the work was completed in $a+b+c$ hours. Imagine that all this time they worked together. How many holes will they dig in total? In the first $a$ hours, the first worker will dig his share of the "total" hole, while the other two will dig half a hole during this time. In the next $b$ hours, the second worker will complete his part of the work, and the others will dig another half a hole. Finally, the third worker (in $c$ hours) will finish his part of the work, and the others will dig another half a hole. In total, 2.5 holes will be dug. Therefore, working together, they would dig a hole 2.5 times faster.