# Time and Distance

Ankur Kulhari

Important Formulas:

1. Speed = Distance / Time

{To remember it, have you ever seen speedometer of any vehicle? In the speedometer “Kmph” is written in the center. That is the unit of speed.
Kmph = Kilo meter per hour

• Kilo meter / hour
• Distance / Time
1. Distance = Speed * Time

If a vehicle covers certain distance d km with a speed of v1 km/hr and further covers same distance d with a speed v2 km/hr, then the average speed of the vehicle is:

Average Speed = 2v1v2 / v1+v2

Explanation:

Overall Speed = Overall Distance / Overall Time

Time = t1+t2 {t1 is the time taken to cover first d distance and t2 is the time taken to cover next d distance.}

Time = Distance / Speed

t1 = d/v1

t2 = d/v2

Overall Time = d(1/v1 + 1/v2)

Overall Distance = d+d = 2d

Overall Speed = 2d/[d(1/v1 + 1/v2)]

= 2v1v2/(v1+v2)

Note:

1. The average speed is not the average of two speeds i.e. x+y/2.
2. While solving questions, take care that all units must be same.
3. Units of speed can be km/hr, m/sec, m/min or km/min etc.
4. Conversion of km/hr to m/sec and m/sec to km/hr

km/hr = (d*1000/3600) m/sec

= (d*10/36) m/sec

= (d*5/18)     {need to multiply 5/18}
5. Similarly, m/sec = (d*18/5) km/sec

Note:

A car covers a distance d km in t1 hours time at a speed of v1 km/hr.
If the car slow down its speed => time taken will be more than t1

speed = k. 1/time {for the same distance}

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 traveling 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 traveled = Average speed * Time

⇒ Distance Traveled = (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

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