3. Four passengers traveled by taxi in the same direction, to four places that were equally distant from their neighboring places. The first passenger, upon exiting, paid a quarter of the amount shown by the taxi meter at that moment, the second passenger paid a third, and the third and fourth passengers each paid half of the amount shown by the taxi meter when they exited the car. Did the taxi driver charge more or less than if he had driven one of the passengers the entire route, and by how much?
Solution. When the passengers got in, the taxi driver turned on the taximeter, which showed an amount of $x$ denars. Upon passing the distance to the first, then the second, third, and fourth location, the price always increased by $u$ denars. Thus, the passengers paid in sequence:

$$
\frac{1}{4}(x+y), \frac{1}{3}(x+2 y), \frac{1}{2}(x+3 y), \frac{1}{2}(x+4 y)
$$

The cost of the ride is $x+4 y$ denars, and the passengers collectively paid

$$
\frac{1}{4}(x+y)+\frac{1}{3}(x+2 y)+\frac{1}{2}(x+3 y)+\frac{1}{2}(x+4 y)=x+4 y+\frac{7}{12} x+\frac{5}{12} y
$$

denars. The taxi driver overcharged by about 50% of the actual cost.