7. (10 points) An industrial robot travels from point $A$ to point $B$ according to a pre-determined algorithm. The diagram shows a part of its repeating trajectory. Determine how many times faster it would reach from point $A$ to point $B$ if it moved in a straight line at twice the speed?

![](https://cdn.mathpix.com/cropped/2024_05_06_0588747f110ff428b268g-7.jpg?height=205&width=851&top_left_y=2396&top_left_x=705)
Answer: 3.33 times.

Solution. The time spent by the robot moving along the given trajectory:

$t_{1}=N \frac{2 a+a+a+a}{v}=5 \frac{N a}{v}$.

The time spent by the robot moving in a straight line:

$t_{2}=N \frac{2 a+a}{2 v}=1.5 \frac{N a}{v}$.

We get that the robot will arrive $\frac{t_{1}}{t_{2}}=3.33$ times faster.