船河问题 - 例题详解

题1 - 静水中船的速度为16公里/小时。如果水流速度为4公里/小时，求其顺流和逆流速度。

答案 - B

解析

Downstream Speed = u + v = 16 + 4 = 20 km/hr
Upstream Speed = u - v = 16 - 4 = 12 km/hr

题2 - 一个人可以以18公里/小时的速度顺流而下，以12公里/小时的速度逆流而上。求其静水速度和水流速度。

答案 - C

解析

Speed of the boat or swimmer in still water = 1/2 * (Downstream Speed + Upstream Speed)
 = 1/2 * (18+12)
 = 15 km/hr
Speed of the current  = 1/2 * (Downstream Speed - Upstream Speed)
 = 1/2 * (18-12)
 = 3 km/hr

题3 - 一个人在4小时内顺流游了28公里，在3小时内逆流游了12公里。求其静水速度和水流速度。

答案 - B

解析

Downstream Speed (u) = 28/4 = 7 km/hr
Upstream Speed (v) = 12/3  = 4 km/hr
Speed of the boat or swimmer in still water = 1/2*(Downstream Speed + Upstream Speed)
 = 1/2*(7+4)
 = 5.5 km/hr
Speed of the current  = 1/2*(Downstream Speed - Upstream Speed)
 = 1/2*(7-4)
 = 1.5 km/hr

题4 - 静水中船的速度为15公里/小时。到某一点逆流所需时间是返回出发点顺流所需时间的两倍。求水流速度。

答案 - B

解析

Let speed of the current = S km/hr.

As per question,
Downstream Speed = 2*Upstream speed
15 + S = 2(15 - S)
S = 3 km/hr

题5 - 一艘船顺流行驶一定距离需要6小时，逆流返回出发点需要8小时。如果水流速度为3公里/小时，求静水速度。

答案 - C

解析

t1 = 6 hrs
t2 = 8 hrs
v = 3 km/hr
u = ?

We know, 
(u + v)t1 = (u - v)t2

(u + 3)6 = (u - 3)8
u = 3 km/hr

题6 - 恒河的水流速度为5公里/小时。一艘机动船逆流航行28公里，然后顺流返回出发点。如果其静水速度为9公里/小时，求总航行时间。

答案 - C

解析

We know, Downstream speed = u + v = 9 + 5 = 14 km/hr
Upstream Speed = u - v = 9 - 5 = 4 km/hr

Speed = Distance/Time
∴ Time = Distance/Speed
∴ Total time taken = t1 + t2
= 28/4 + 28/14
= 7 + 2 = 9 hr

题7 - 一艘船逆流航行32公里，顺流航行60公里，共需9小时。它逆流航行40公里，顺流航行84公里，共需12小时。求静水速度和水流速度。

答案 - A

解析

Let, upstream speed = u km/hr
Downstream speed = d km/hr

32/u + 60/d = 9   (Time = Distance/Speed)

Simlarly,
40/u + 84/d = 12

32x + 60y = 9  ...(i)   (Assuming 1/u = x and 1/d = y)
40x + 84y = 12 ...(ii)

(Equation(ii) * 4) - (Equation (i)*5), we get, 
y = 1/12. So, x = 1/8

Hence, downstream speed = 12 km/hr
Upstream speed = 8 km/hr

So,
Speed of the boat in still water = 1/2*(12+8) = 10 km/hr
Speed of the current = 1/2*(12 - 8) = 2 km/hr

题8 - 游泳者在静水中的速度为12公里/小时。游到某地再返回出发点共需6小时。水流速度为4公里/小时。求两点间的距离。

答案 - B

解析

Let distance = D
Downstream time = t1; Downstream Speed = 1/2*(12+4) = 8 km/hr
Upstream Time = t2; Upstream Speed = 1/2*(12-4) = 4 km/hr

Total time = t1 + t2
6 = (D/Upstream speed) + (D/Downstream speed)
6 = D/8 + D/4
D = 16 km

题9 - 一艘船顺流行驶30公里需要2小时。返回时逆流行驶相同距离需要6小时。如果水流速度是船速的一半，求船速。

答案 - C

解析

Downstream Speed = 30/2 = 15 km/hr
Upstream Speed = 30/6 = 5 km/hr
Speed of the boat in still water = 1/2*(downstream speed + upstream speed)
= 1/2*(15+5)
= 10 km/hr

题10 - 一艘轮船顺流从一点到另一点需要4小时。逆流行驶相同距离需要5小时。如果水流速度为2公里/小时，求两点间的距离。

答案 - D

解析

Let the distance be D km.
∴ Downstream Speed = D/4 km/hr
And Upstream Speed = D/5 km/hr
Given, Speed of current = 2 km/hr

Speed of the current  = 1/2*(Downstream Speed - Upstream Speed)
2 = 1/2*(D/4 - D/5)
D = 80 km

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