速度与距离 - 例题详解

题1 - 54公里/小时是多少米/秒？

答案 - A

解释

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

题2 - 16米/秒是多少公里/小时？

答案 - C

解释

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

题3 - 安妮塔以4公里/小时的速度走完路程的2/3，然后以5公里/小时的速度走完剩下的路程，共用了1小时24分钟。求总路程。

答案 - D

解释

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

题4 - 一个男人从家步行到火车站。如果他以5公里/小时的速度步行，他会错过火车7分钟。但是，如果他以6公里/小时的速度步行，他会比火车发车提前5分钟到达车站。求他到车站的路程。

答案 - B

解释

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

题5 - 一列火车以其正常速度的7/8行驶，比预计到达时间晚了10分钟。求其正常行驶时间。

答案 - B

解释

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.

题6 - 希特什开车以70公里/小时的速度行驶一段距离，然后骑自行车以55公里/小时的速度返回起点。求他全程的平均速度。

答案 - B

解释

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

题7 - A站和B站相距450公里。一列火车下午4点从A站出发，以60公里/小时的匀速向B站行驶。另一列火车下午3点20分从B站出发，以80公里/小时的匀速向A站行驶。两列火车将在距离A站多远的地方相遇，以及什么时间相遇？

答案 - A

解释

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

题8 - 一个男人骑自行车从A地到B地，相距21公里，用了1小时40分钟。从A地到B地，前13公里路段是平路，之后是上坡路。该男子在平路上平均速度为15公里/小时。求他在上坡路段的平均速度。

答案 - A

解释

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

题9 - 一个罪犯被警察从100米外发现。当警察开始追捕时，罪犯也开始逃跑。如果罪犯的速度是8公里/小时，警察的速度是10公里/小时，那么罪犯在被抓住之前跑了多远？

答案 - C

解释

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

题10 - 我步行一段距离，然后骑车返回，总共用了37分钟。如果我步行往返，需要55分钟。那么骑车往返需要多少分钟？

答案 - B

解释

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.

题11 - A站和B站相距390公里。上午10点，一列火车从A站出发，以65公里/小时的速度向B站行驶。上午11点，另一列火车从B站出发，以35公里/小时的速度向A站行驶。它们将在几点相遇？

答案 - A

解释

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

题12 - 一列货运列车在某一时间以固定的速度离开车站。6小时后，一列快车从同一车站出发，以90公里/小时的匀速沿同一方向行驶。这列快车在4小时内追上了货运列车。求货运列车的速度。

答案 - B

解释

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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