Concepts And Problem Of Time And Distance

1) There is a relationship between speed, distance and time:

Speed = Distance / Time OR
Distance = Speed* Time

2) Average Speed = 2xy / x+y
where x km/hr is a speed for certain distance and y km/hr is a speed at for same distance covered.

**** Remember that average speed is not just an average of two speeds i.e. x+y/2. It is equal to 2xy / x+y

3) Always remember that during solving questions units must be same. Units can be km/hr, m/sec etc.
**** Conversion of km/ hr to m/ sec and m/ sec to km/ hr
x km/ hr = (x* 5/18) m/sec i.e. u just need to multiply 5/18
Similarly, x m/sec = (x*18/5) km/sec

4) As we know, Speed = Distance/ Time. Now, if in questions Distance is constant then speed will be inversely proportional to time i.e. if speed increases ,time taken will decrease and vice versa.

Time and Distance Problems
Problem 1: A man covers a distance of 600m in 2min 30sec. What will be the speed in km/hr?
Solution: Speed =Distance / Time
⇒ Distance covered = 600m, Time taken = 2min 30sec = 150sec
Therefore, Speed= 600 / 150 = 4 m/sec
⇒ 4m/sec = (4*18/5) km/hr = 14.4 km/ hr.

Problem 2: A boy travelling from his home to school at 25 km/hr and came back at 4 km/hr. If whole journey took 5 hours 48 min. Find the distance of home and school.

Solution: In this question, distance for both speed is constant.
⇒ Average speed = (2xy/ x+y) km/hr, where x and y are speeds
⇒ Average speed = (2*25*4)/ 25+4 =200/29 km/hr
Time = 5hours 48min= 29/5 hours
Now, Distance travelled = Average speed * Time
⇒ Distance Travelled = (200/29)*(29/5) = 40 km
Therefore distance of school from home = 40/2 = 20km.

Problem 3: Two men start from opposite ends A and B of a linear track respectively and meet at point 60m from A. If AB= 100m. What will be the ratio of speed of both men?
Solution: According to this question, time is constant. Therefore, speed is directly proportional to distance.
Speed∝Distance

⇒ Ratio of distance covered by both men = 60:40 = 3:2
⇒ Therefore, Ratio of speeds of both men = 3:2

Problem 4: A car travels along four sides of a square at speeds of 200, 400, 600 and 800 km/hr. Find average speed.
Solution: Let x km be the side of square and y km/hr be average speed
Using basic formula, Time = Total Distance / Average Speed
x/200 + x/400 + x/600 + x/800 = 4x/y ⇒ 25x/ 2400 = 4x/ y⇒ y= 384
⇒ Average speed = 384 km/hr