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

Speed basically tells us 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.

Speed = Distance/Time

This shows that Speed is directly proportional to distance but inversely proportional to time.

Distance = Speed * Time and,

Time = Distance/Speed

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

The important point to note is that time given was in minutes, whereas the speed was in kmph.

Therefore, either speed has to be converted to km/min or time has to be expressed in hours.

We have converted time in hours.

15 min=15/60 hours.

The average speed of travelling at two different speeds for the same time span is just the simple average of two speeds.

Let Speed 1 be x km/hr

Let Speed 2 be y km/hr

Therefore,

Average Speed when time is same = (x+y)/2

As the time is same, i.e. 1 hour,

Average speed= (45+65)/2= 55 kmph.

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Average Speed = 2ab/(a+b) (where a and b are two speeds)

Let us understand how this came.

Let the two speeds be a km/hr and b km/hr.

Let 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/hr will be x/a hrs

And, time taken to cover x km at b km/hr will be x/b hrs

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

And the total distance covered = 2x

Therefore,

Average Speed =

37.5 kmph is incorrect as the time travelled is different in both the cases and only the distances are same.

Let distance = x km

Therefore, Time taken on Big Bull's onward journey =x/30 hours and

Time taken on his return journey=x/45 hours

Therefore, total time = (x/30)+ (x/45) hours.

Total distance = 2x km

Average speed= kmph = 36kmph

1 km = 1000 meters

1 meter = 100 cm

1 hour = 60 minutes

1 min = 60 seconds

1 hours = 3600 seconds

1 km/hr = m/sec

Hence, 1 m/sec = km/hr

1 mile = 1760 yards

1 yard = 3 feet

1 mile = 5280 feet

1 mph = yards/sec

1 mph = ft/sec

Now, let us try doing some questions.

We know that 1 hour = 60 minutes

Therefore, 15 minutes = 1/4 hours (because 15/60 = 1/4)

Distance = Speed * Time

Distance = 40 * (1/4) = 10 kms

60 = 50 * T

T = 1.2 hrs or 1 hr and 12 minutes

Let his usual speed be x km/hr and his usual time be t hours

His time on this occasion is

The time taken is hrs

Since the distance travelled on both occasions is the same,

xt = * ( because, Distance = Speed * Time)

Solving for t, we get t = 5/6hrs

= 50 minutes and the time taken on this occasion = 50 + 10 = 60 minutes

Therefore, Average Speed =

Average Speed = 36 kmph

As Distance ∞ Speed

Distance travelled by CTU bus : Distance travelled by ordinary bus :: 3:2

Let the distance travelled between Ambala and Lalru be x km

Then the distance travelled by CTU bus = 32 + x

While the distance travelled by ordinary bus = 32 – x

Therefore, 32 + x : 32 – x :: 3:2

Solving for x, we get x = 6.4 km (i.e. the distance between Ambala and Lalru)

Therefore,

Solving for t, we get t = 3 hrs

Since the usual time taken = 3 hrs, usual distance travelled = 3S kms

Equating distance travelled usually, with distance travelled at any of the other two speeds, we get 6 * (3+20/60) = 3S

Therefore, S = 6 kmph

Hence, 108 kmph = 108 * m/sec = 30 m/sec

Distance = Speed * Time

360 = 30 * Time

Time = 12 secs