### Time Distance And Speed

In this article, we will discuss the concepts, formulas and some questions based on speed, time and distance. As Time, Speed and Distance form an important part of every competitive exam, you cannot afford to skip this topic.

### Speed

Speed basically: how fast or slow an object moves.

It is described as the distance travelled by an object divided with the time taken to cover that distance. The distance covered per unit time is called speed.

Speed is directly proportional to distance.
Speed is inversely proportional to distance.

Speed = Distance Time

Speed is directly proportional to distance but inversely proportional to time.

Distance = Speed * Time
Time = Distance Speed

### Average Speed

The average speed is given by total distance divided by total time.

Average Speed = Total Distance Total Time

### How to convert units:

km/h convert  into m/s = multiplied by 5/18

m/s convert into km/h = multiplied by 18/5

where, km = kilometer, h = hour, m = minute, s = second

Example: What is the distance covered by a car travelling at a speed of 40 km/h in 15 minutes?

Solution:

Distance= speed* time= 40*15/60=10 km.

Note  time given in minutes, whereas the speed was in km/h.

So, I want to convert minute into hour

15 min=15/60 hours.

Average Speed in different case:

Case 1: When Time is Constant

The average speed of travelling at two different speeds for the same time is the average of two speeds.
Speed 1 be X km/h, Speed 2 be Y km/h
Therefore,
Average Speed = (x+y)2

Example: A car is travelling at an average speed of 45km/h for the 1h and at 65 km/h for the next 1h. Calculate his average speed.

Solution:
As the time is same i.e. 1 hour,
Average speed= (45+65)/2= 55 km/h.

Case 2: Average Speed When Distance is Constant

Average Speed = 2ab (a+b)

Where a and b are two speeds.

The two speeds be a km/h and b km/h.

The distance travelled in each of the speeds be x km.

As we know that,

Time = Distance/Speed

Hence,

Time taken to cover x km at a km/h will be x/a h

And,

Time taken to cover x km at b km/h will be x/b h

Total time taken = x/a+x/b = (bx+ax)/ab = x(b+a)/ab

total distance covered = 2x

Therefore,

Average Speed = 2xab/x(b+a)=2ab(a+b)

Example: On his way to office, Big cow was travelling at 30 km/h and on the return journey, he was travelling at 45kmph. What is Big cow’s average speed?

Solution:

Let distance = x km

Therefore, Time taken on Big cow’s journey =x/30 hours and

Time has taken on return journey=x/45 hours

Therefore,

Total time = (x/30) + (x/45) hours.

Total distance = 2x km

Average speed = 2x divided by (x/30+x/45)km/h = 36km/h

Important Time and Distance Conversions

1 km = 1000 meters

1 meter = 100 cm

1 hour = 60 minutes

1 min = 60 seconds

1 hours = 3600 seconds

1 km/hr = 1*1000/1*3600 m/s

Hence,

1 m/sec = 1*1000/1*3600 km/h

1 mile = 1760 yards

1 yard = 3 feet

1 mile = 5280 feet

1 mph = 1*1760/1*3600 = 22/45yards/sec

1 mph = 1*5280/1*3600 = 22/15ft/sec

Some questions:

1).A man went from home to office at a speed of 40 km/h and came back with a speed of 60 km/h find the average speed during the whole journey?

Solution:
Average Speed = 2xy (x+y)
S avg.= 2x40x60 40+60 = 2405 = 48 km/h

2).If a man travels with a speed of 15 km/h instead of 10 km/h, then he travel 20 km more in the same time period. How much distance did he travel?

Solution: by the ratio method:

S1:S2 = 15:10 (where, S1=First Speed, S2= Second Speed)

Then, S1:S2 = 3:2

Hence, D1:D2 = 3:2 (where, D1,D2 = First and Second distance )

D1:D2 = 3:2 (Because D=ST , distance is directly proportional to speed )

D2 = 20km/1*2 =  40 km.

3). The average speed of a bus excluding the stoppage is 54 km/h and the average speed of the bus including the stoppage is 45 km/h .then how many minutes did the bus stopper hour?

Solution:   Excluding Stoppage = 54 km per hour

Including Stoppage = 45 km per hour

Difference is 9 km distance,

Stop time = 9/54 = 1/6 h

In a question asked, in minutes so, 1/6*60 = 10 minutes.