37. Two people, who have one bicycle, need to get from point $A$ to point $B$, which is 40 km away from $A$. The first person walks at a speed of 4 km/h and rides the bicycle at 30 km/h, while the second person walks at a speed of 6 km/h and rides the bicycle at 20 km/h. What is the minimum time they can take to reach point $B$? (The bicycle can be left unattended.)
37. Let the first person travel $x$ hours by vehicle and $y$ hours on foot, then the second person travels $y$ hours by vehicle and $x$ hours on foot. We have the equation $30 x + 4 y = 20 y + 6 x$, from which $x = \frac{2}{3} y$. Therefore, the first person walked $y$ hours and traveled $\frac{2}{3} y$ hours by vehicle, while the second person walked $\frac{2}{3} y$ hours and traveled $y$ hours by vehicle. Knowing the total distance, we can form the equation $4 y + \frac{2}{3} y \cdot 30 = 40$, from which $y = \frac{5}{3}$ hours. The first person was on the road for $\frac{5}{3} + \frac{2}{3} \cdot \frac{5}{3} = 2 \frac{7}{9}$ (hours), and the second person was on the road for the same amount of time, as he walked $1 \frac{1}{9}$ hours and traveled $1 \frac{2}{3}$ hours. Therefore, the minimum time it takes for them to reach point $B$ is 2 hours 46 minutes 40 seconds.