题目
A boat travels from Point A to Point B in the direction of water and then returns to Point A. In still water, the boat travels at a speed of 28 kilometers per hour. If the speed of the water current is 4 kilometers per hour and the time taken for the round-trip is 2 hours and 55 minutes, what is the total distance traveled by the boat in the round trip ?
解析
一艘船顺水从A点行驶到B点,然后逆水返回A点。在静水中,船的速度是每小时28千米。如果水流速度是每小时4千米,往返所用时间是2小时55分钟,那么船往返行驶的总距离是多少?
已知船在静水中速度\(v = 28\)千米/小时,水流速度\(u=4\)千米/小时。
顺水速度\(v_{顺}=v + u=28 + 4=32\)千米/小时;
逆水速度\(v_{逆}=v - u = 28-4 = 24\)千米/小时。
设从A到B的距离为\(d\)千米,根据时间 = 距离÷速度,往返总时间\(t = t_{顺}+t_{逆}\)。
已知往返总时间\(t = 2\)小时\(55\)分钟,将其转化为小时为\(t=\frac{2\times60 + 55}{60}=\frac{175}{60}=\frac{35}{12}\)小时。
则\(\frac{d}{32}+\frac{d}{24}=\frac{35}{12}\)
对\(\frac{d}{32}+\frac{d}{24}=\frac{35}{12}\)进行求解,先通分得到\(\frac{3d + 4d}{96}=\frac{35}{12}\),即\(\frac{7d}{96}=\frac{35}{12}\),解得\(d = 40\)千米。
往返总距离为\(2d=2\times40 = 80\)千米
综上,答案是C选项。