13.078. A tourist traveled $5 / 8$ of the total distance by car and the remaining part by boat. The boat's speed is 20 km/h less than the car's speed. The tourist traveled by car for 15 minutes longer than by boat. What are the speeds of the car and the boat if the total distance of the tourist's journey is 160 km?
## Solution.

The tourist drove 160 * 5/8 = 100 km by car, and 160 - 100 = 60 km by boat. Let \( x \) km/h be the speed of the boat, and \( 20 + x \) km/h the speed of the car. The tourist traveled by car for \( \frac{100}{20+x} \) hours, and by boat for \( \frac{60}{x} \) hours. According to the problem, \( \frac{100}{20+x} - \frac{60}{x} = 0.25 \), from which \( x = 60 \) or \( x = 80 \).

Answer: the speed of the car is 100 or 80 km/h; the speed of the boat is 80 or 60 km/h.