速度與距離 - 例題詳解

題1 - 54公里/小時是多少米/秒？

答案 - A

解釋

54 km/hr = (54*5/18) m/sec = 15 m/sec.

題2 - 16米/秒是多少公里/小時？

答案 - C

解釋

16 m/sec = (16*18/5)km/hr = 288/5km/hr =57.6 km/hr.

題3 - 安妮塔以4公里/小時的速度走完路程的2/3，然後以5公里/小時的速度走完剩下的路程，共用了1小時24分鐘。求總路程。

答案 - D

解釋

Let the aggregate separation be x km.  
Then, 2/3x/4+1/3x/5=7/5
=> x/6+x/15=7/5
=> 5x+2x=42
=> 7x=42
=> x=6. 
∴ Total separation = 6 km

題4 - 一個男人從家步行到火車站。如果他以5公里/小時的速度步行，他會錯過火車7分鐘。但是，如果他以6公里/小時的速度步行，他會比火車發車提前5分鐘到達車站。求他到車站的路程。

答案 - B

解釋

Let the required separation be x km. At that point, 
X/5 - x/6 = 12/60 (distinction between two time interims is 12 min.) 
=> x/5 - x/6 = 1/5 
=> 6x-5x=6 
=> x= 6 
Required separation = 6 kms

題5 - 一列火車以其正常速度的7/8行駛，比預計到達時間晚了10分鐘。求其正常行駛時間。

答案 - B

解釋

New speed = 7/8 of its standard velocity 
New time taken = 8/7 of the standard time. 
(8/7 of the standard time)- (common time) = 10 min. 
=> 1/7 of the standard time = 10 min 
=> usual time = 70 min.

題6 - 希特什開車以70公里/小時的速度行駛一段距離，然後騎腳踏車以55公里/小時的速度返回起點。求他全程的平均速度。

答案 - B

解釋

Normal velocity = 2xy/(x+y) km/hr = (2*70*55)/ (70+55) km/hr 
= (2*70*55)/125 km/hr = 308/5 km/hr = 61.6 km/hr

題7 - A站和B站相距450公里。一列火車下午4點從A站出發，以60公里/小時的勻速向B站行駛。另一列火車下午3點20分從B站出發，以80公里/小時的勻速向A站行駛。兩列火車將在距離A站多遠的地方相遇，以及什麼時間相遇？

答案 - A

解釋

Assume two trains meet at x km from A 
(time taken by B to cover (450-x) km-(time taken by A to cover x km) = 40/60 
=> (450-x)/80 - x/60 = 40/60 ?3 (450-x) - 4x = 160 
=> 7x=1190 ∴ x = 170 	
In this way the two trains meet at a separation of 170 km from A. 
Time taken by A to cover 170 km = 170/60 = 2hrs 50 min. 
Along these lines, the two trains meet at 6:50 pm

題8 - 一個男人騎腳踏車從A地到B地，相距21公里，用了1小時40分鐘。從A地到B地，前13公里路段是平路，之後是上坡路。該男子在平路上平均速度為15公里/小時。求他在上坡路段的平均速度。

答案 - A

解釋

Let the normal tough rate be x km/hr. at that point, 
13/15 + 8/x = 5/3 
=>8/x= (5/3-13/15) = 12/15 = 4/5 
=>x = (8*5)/4 = 10 
∴ Normal tough rate = 10 km/hr

題9 - 一個罪犯被警察從100米外發現。當警察開始追捕時，罪犯也開始逃跑。如果罪犯的速度是8公里/小時，警察的速度是10公里/小時，那麼罪犯在被抓住之前跑了多遠？

答案 - C

解釋

Relative pace of the policeman = (10-8) km/hr = 2 km/hr 
Time taken by policeman to cover 100 m = (100/1000*1/2) hr = 1/20 hr 
In 1/20 hr, the cheat covers a separation of (8*1/20) km= (2/5 km) = (2/5*1000) m = 400 m

題10 - 我步行一段距離，然後騎車返回，總共用了37分鐘。如果我步行往返，需要55分鐘。那麼騎車往返需要多少分鐘？

答案 - B

解釋

Let the given separation be x km. At that point, 
(Time taken to walk X km)+ (time taken to ride x km) = 37 min. 
=> (time taken to walk 2X km) + (time taken to ride 2x km) = 74 min. 
=> 55 min + (time taken to ride 2 x km) = 74 
=> time taken to ride 2x km = 19 min.

題11 - A站和B站相距390公里。上午10點，一列火車從A站出發，以65公里/小時的速度向B站行駛。上午11點，另一列火車從B站出發，以35公里/小時的速度向A站行駛。它們將在幾點相遇？

答案 - A

解釋

Assume they meet x hours after 10 am then, 
(separation moved by first in x hrs.) + (separation moved by second in (x-1) hrs) = 390 
∴ 65x+ 35(x-1) = 390 
=> 100x =425 
=> x= 17/4 
In this way, they meet 4 hrs 15 min. after 10 am at 2.15 pm

題12 - 一列貨運列車在某一時間以固定的速度離開車站。6小時後，一列快車從同一車站出發，以90公里/小時的勻速沿同一方向行駛。這列快車在4小時內追上了貨運列車。求貨運列車的速度。

答案 - B

解釋

Let the velocity of the merchandise train be x kmph. 
Separation secured by products train in 10 hours = separation secured by express prepare in 4 hours 
∴ 10x =4*90 or x = 36 
Along these lines, rate of products train = 36 kmph

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