jmc

Since $\text{work}=\text{rate}\times \text{time}$, let $r$ be the rate at which one worker can built an embankment. It follows that 1 embankment takes $$1\text{ embankment}=(75r)\times (4\text{days})$$ so $r=\frac{1}{4\cdot 75}.$ If only $50$ workers were available, then $$1\text{ embankment}=(50r)\times (t\text{days})$$ so $$t=\frac{1}{50\cdot \frac{1}{4\cdot 75}}=\frac{300}{50}=\boxed{6}\text{days}.$$ Notice that the number of days and the number of workers are inversely related.