13.124. Two steamers left the port simultaneously, with one heading south and the other heading east. After 2 hours, the distance between them was 174 km. Find the average speed of each steamer, given that one of them traveled 3 km more on average per hour,

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-864.jpg?height=354&width=598&top_left_y=333&top_left_x=633)

Fig. 13.8 than the other.
## Solution.

Let $x$ km/h be the speed of the second steamboat, and $x+3$ km/h be the speed of the first. In 2 hours, the first steamboat traveled $2(x+3)$ km, and the second $2x$ km. From the right triangle (Fig. 13.8), by the Pythagorean theorem, $(2x)^2 + (2(x+3))^2 = 174^2$, from which $x = 60$ km/h.

Answer: 60 and 63 km/h.