船河問題 - 例題詳解

題1 - 靜水中船的速度為16公里/小時。如果水流速度為4公里/小時，求其順流和逆流速度。

答案 - B

解析

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

題2 - 一個人可以以18公里/小時的速度順流而下，以12公里/小時的速度逆流而上。求其靜水速度和水流速度。

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

題3 - 一個人在4小時內順流遊了28公里，在3小時內逆流遊了12公里。求其靜水速度和水流速度。

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

題4 - 靜水中船的速度為15公里/小時。到某一點逆流所需時間是返回出發點順流所需時間的兩倍。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

題5 - 一艘船順流行駛一定距離需要6小時，逆流返回出發點需要8小時。如果水流速度為3公里/小時，求靜水速度。

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

題6 - 恆河的水流速度為5公里/小時。一艘機動船逆流航行28公里，然後順流返回出發點。如果其靜水速度為9公里/小時，求總航行時間。

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

題7 - 一艘船逆流航行32公里，順流航行60公里，共需9小時。它逆流航行40公里，順流航行84公里，共需12小時。求靜水速度和水流速度。

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

題8 - 游泳者在靜水中的速度為12公里/小時。游到某地再返回出發點共需6小時。水流速度為4公里/小時。求兩點間的距離。

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

題9 - 一艘船順流行駛30公里需要2小時。返回時逆流行駛相同距離需要6小時。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

題10 - 一艘輪船順流從一點到另一點需要4小時。逆流行駛相同距離需要5小時。如果水流速度為2公里/小時，求兩點間的距離。

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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