Time, Speed and Distance: Concepts and Problems

Concepts

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

Let's do some Time and Distance problems, in case you face any difficulty then post a comment in comments section.

1.

How many minutes Raman will take to cover a distance of 400 meters if he runs at a speed of 20 km/hr ?

• A.
  2 mins
• C.
  1⅕ mins
• E.
  1.5 mins

• B.
  2.5 mins
• D.
  None of these

• Answer & Explanation

Answer : [C]
Explanation :
⇒ Raman's speed = 20 km/hr = 20 × 5/18 = 50/9 m/sec
⇒ 400 × 9/50 = 1⅕ mins

2.

John travelled from his town to city.  John went to city by bicycle at the speed of 25 km/h and came back at the speed of 4 km/h. If John took 5 hours and 48 min to complete his journey, what is the distance between town and city ?

• A.
  15 km
• C.
  20 km

• B.
  22 km
• D.
  25 km

• Answer & Explanation

Answer : [C]
Explanation :
⇒ Average speed of John = 2xy/x+y =  2 × 25 × 4 / 25 + 4= 200/29 km/h
⇒ Distance traveled = Speed × Time = 200/29 × 29/5 = 40 Km
⇒ Distance between city and town = 40/2 = 20 km

3.

Speed of a train is 20 meters per second. It can cross a pole in 10 seconds. What is the length of train ?

• A.
  150 m
• C.
  200 m

• B.
  250 m
• D.
  300 m

• Answer & Explanation

Answer : [C]
Explanation : 
⇒ Lenght of train = 20 × 10 = 200 meters

4.

Ram walks at a speed of  12 km/h. Today the day was very hot so walked at ⅚ of his average speed. He arrived his school 10 minutes late. Find the usual time he takes to cover distance between his school and home ?

• A.
  40 mins
• C.
  50 mins

• B.
  45 mins
• D.
  60 mins

• Answer & Explanation

Answer : [C]
Explanation :
⇒ If Ram is walking at ⅚  of his usual speed that means he is taking 6/5 of using time.
⇒ 6/5 of usual time - usual time = 10 mins
⇒ 1/5 of usual time = 10 mins
⇒ Usual time = 50 mins

5.

A car running at 65 km/h takes one hour to cover a distance. If the speed is reduced by 15 km/hour then in how much time it will cover the distance  ?

• A.
  72 mins
• C.
  76 mins

• B.
  78 mins
• D.
  None of these

• Answer & Explanation

Answer : [B]
Explanation :
⇒Reduced speed = 65-15 = 50 km/h
⇒ Now car will take 65/50 × 60 mins = 78 mins

6.

In a 100 m race A runs at a speed of 1.66 m/s. If A gives a start of 4m to B and still beats him by 12 seconds. What is the speed of B  ?

• A.
  1 m/s
• C.
  1.25 m/s

• B.
  1.33 m/s
• D.
  Rs 1.5 m/s

• Answer & Explanation

Answer : [B]
Explanation :
⇒Time taken by A to cover 100 meters = 60 seconds
⇒ Since A gives a start of 4 seconds then time takes by B = 72 seconds
⇒ B takes 72 seconds to cover 96 meters
⇒ Speed of B = 96/72 = 1.33 m/s

7.

In a kilometer race, A beats B by 100 meters. B beats C by 100 meters. By how much meters does A beat C in the same race ?

• A.
  200 meters
• C.
  190 meters

• B.
  180 meters
• D.
  210 meters

• Answer & Explanation

Answer : [C]
Explanation :
⇒ While A covers 1000 meters, B can cover 900 meters 
⇒ While B covers 1000 meters, C can cover 900 meters
⇒ Lets assume that all three of them are running same race. So when B runs 900 meters, C can run 900 × 9/10 =810
⇒ So A can beat C by 190 meters.